Chapter 4. Purchasing a Pizza The probability that a customer selects a pizza with mushrooms or pepperoni is 0.55, and the probability that the customer selects only mushrooms is 0.32. Conditional Probability and Cards A standard deck of cards has: 52 Cards in 13 values and 4 suits Suits are Spades, Clubs, Diamonds and Hearts Each suit has 13 card values: 2-10, 3 “face cards” Jack, Queen, King (J, Q, K) and and Ace (A) Improve this answer. When two dice are rolled, find the probability of getting a greater number on the first die than the one on the second, given that the sum should equal 8. 3. the pancake house uses 17 packages of bacon in the morning and 21 packages in the afternoon. 4 CHOOSE 3 = 4 possible combinations. The number of permutations with repetitions in this set is 36. 14. They are shuffled into a random order. Find the probability that the company accepts the shipments when sampling with replacement. Out of these 2400 names, 600 of them are Juniors. and A is the event of interest. Our ratio calculator can be quite helpful in finding the missing term of such ratios! Chapter 3: Probability. Help on math! 40% 10% 8% 2% Ajar has 20 marbles: 3 green, 12 blue, 5 red. What is the probability of choosing an even number from the numbers 1, 2,3,4,5? The numbers 4 through 14 are placed in a Number of All possible choice is 6 and number of your favourable choice is 2 so Ans 2/6=1/3 Hypergeometric: televisions. I’m going to use the formula above: The number of trials (n) is 5, the probability of getting a defective machine (p) is 4/10, so q is 6/10, and x = 5. appc JWBK121-Mun March 18, 2008 3:42 Char Count= APPENDIX C Understanding and Choosing the Right Probability Distributions Plotting data is one method for selecting a probability distribution.The following steps provide another process ⦠Rule 3 deals with the relationship between the probability of an event and the probability of its complement event. Requires basic knowledge of standard playing cards. Tom eats 3 of them, by randomly choosing. If the probability that he or she selects only pepperoni is 0.17, find the probability of the customer selecting both items. Norman A. Answer: What is the probability of choosing a ball other In Experiment 1 the probability of each outcome is always the same. What is the probability of choosing neither white nor green? The first thing to do here is find the total number of students in the contest. The fact that we can document and measure probability illustrates that life is a series of random events. More Problems on probability and statistics are presented. 4th through 7th Grades. There are 3 even numbers, each a multiple of 3, also contributing and there are 3 odd numbers, each a multiple of 3, also contributing. Thus There are 6+3+3 = 12 possible number picks that comply with the selection criteria. Such numbers are 2 ,3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18. Probability as requested = 12/18 = 2/3 = .666666… ~ 66.7% Probability In general: 1/12 B. WHAT IF? This gives 3/7 x 2/6 x 1/5 = 6/210 or 3%. The Similarly, the probability of getting all the numbers from 2,3,4,5 and 6, one at a time is 1/6. Required fields are marked * Similarly, in 3 people case, probability that at least one person gets hat = 1 – P(no one gets hat) = 1 – 1/8 = 7/8. We say that the probability of the coin landing H is ½. 2. Complete the probability distribution table for drawing 1 marble out of the bag. They test to see how many defective lenses they made the time period of January 1 to March 31. probability of choosing a 4, OT REPLACING IT nd then choosing a 4? Also P (A|E 1) = P (drawing a red ball from bag I) = 4/8 = ½. Since we have a total of 52 cards, the probability of selecting a club or a nine is 16 / 52 or approximately 30.8%. In a math class of 30 students, 17 are boys and 13 are girls. If a student is chosen at random from the class, what is the probability of choosing a girl or an A student? Module 21 1114 There are ten marbles in the bag, so the probability of drawing a blue marble is 4/10. I tried question a) is Let A represent Suri , Lily and Violeta are chosen for the group.Let O represent all possible selections.The number of ways... Throwing Dice When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6. Seniors = 300 * 5 = 1500, Juniors = 200 * 3 = 600, Sophomores = 200, and Freshmen = 100. And the probability of the coin landing T is ½ . Mathematics, 21.06.2019 14:10, nunezjazmine01. Question . Number of ways it can happen: 4 (there are 4 blues) Total number of outcomes: 5 (there are 5 marbles in total) So the probability = 4 5 = 0.8. Are these events mutually inclusive? Are A and B independent? Find the probability of choosing 3 blue . Ignoring twins and other multiple births, assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. a.. What is the probability that the next three babies are of the same sex? The probability of any one of them is 16. 4 Example 3: Two cards are drawn without replacement in succession from a well-shuffled deck of 52 playing cards. It is key in the discussion of life by design or accident. Suppose the probability that you win a point is p and this is true independently for all points. Then P (E 1) = P (E 2) = 1/2. 3. There are 6 female and 3 male kittens at an adoption center. * What is the probability of choosing an even number from the numbers 1, 2,3,4,5? Total outcomes=6 Possible outcomes=2 Probability=possible outcomes/total outcomes Probability =2/6=1/3 the probability of getting a 3 or a 4 is 1/3. What is the probability of selecting a mint expressed as a fraction? Kinda a hobby. From 1 to 20 (inclusive) there are 10 even numbers, so the probability of picking an even number is 10/20, or 1/2. There are 6 multiples of 3, so the probability of picking a multiple of 3 is 6/20, or 3/10. What is the probability of picking a 2, EPLACING IT d then choosing a 3? Thus, the probability of any one of them is 1/36. How many ways can this be done? Find the probability that the company accepts the shipments when sampling with replacement. There are two favorable outcomes: 5 and 6 . The number of combinations for sample space 4 CHOOSE 3 can also be written as 4C 3 in the format … This is written as B ⊂ A. Suppose that P (A) = 0.4,P (B) = 0.3 and P ((A ∪ B) C) = 0.42. Probability Examples A jar contains 30 red marbles, 12 yellow marbles, 8 green marbles and 5 blue marbles What is the probability that you draw and replace marbles 3 times and you get NO red marbles? Solution: Let E 1 be the event of choosing the bag I, E 2 be the event of choosing the bag say bag II and A be the event of drawing a red ball. Rolling an even number (2, 4 or 6) is an event, and rolling an odd number (1, 3 or 5) is also an event. A ball is chosen at random. Since there are originally 12 sweets, of which 5 are red. The probability of choosing a purple fl ower and then a yellow fl ower is 1 — 12, or about 8%. The number of ways that Suri , Lily and Violeta can be chosen is n(A) = 3P3 = 3!. probability of getting 3 is 1/6 [as there is only one 3] probability of getting 4 is 1/6 [ there is only one 4] Using addition theorem of of probability , probability of getting 3 or 4 is 1/6 + 1/6 = 2/6 = 1/3. So adding all these up you get a total of 2400 names in the hat. P ( X o r Y) = P ( X) + P ( Y) − P ( X a n d Y) Example. What is the probability of randomly choosing a red or a green marble? Ways of choosing three digits correctly out of 4 is the same choosing one incorrectly. What is the probability of choosing a number from 1 to 10 that is greater than 5 or even? 1. on the student council. edited Jan 14 '17 at 18:00. Find the probability of choosing a red marble, then a … $$P(A) = \frac{n(A)}{n(O)} = \frac{6}{13800} = \frac{1}{2300}$$ The probability Suri , Lily and Violeta will be is $\frac{1}{2300}$. There are six possible outcomes: 1, 2, 3, 4, 5 and 6 . P(Russia) = total number of stamps stamps from Russia _ _ _ _ _ = 13 1 The probability of loosing a stamp from Russia is 1 out of 13. ! View PDF. Your email address will not be published. Thus the probability of drawing 4 aces from a standard deck of 52 cards is. Four kittens are chosen at random. If a student is chosen at random from the class, what is the probability of choosing a girl or an A student? 139 Permutations nPr = n! Please help , I only need the second part of the question Betty picks 4 random marbles from a bag containing 3 white , 4 yellow and 5 blue marbles The probability that exactly 1 of the 4 marbles drawn is blue is (0.3535) . The formula to calculate the theoretical probability of event A happening is: P (A) = number of desired outcomes / total number of possible outcomes. 5. The probability of drawing the 3rd card is 1/5. P(oats) = total boxes of cereal number of oat cereals _ _ _ _ _ _ = 11 4 The probability of choosing an oat cereal is 4 out of 11. The number of possible orders for three cards is 3! You can only use the classical probability formula when all events are equally likely. probability of choosing a king or a club? What is the probability of the outcomes summing to five? probability • In this chapter, we will study the topic of probability which is used in many different areas including ... (5,2), (4,3) • (3,4)} There are six ways two obtain a sum of seven. So the probability is: P ( … What is the probability of choosing an even number from the numbers 1, 2,3,4,5? Does the proposed process correctly simulate the random selection of 3 women from a group of 9 people Stack Exchange network consists of 178 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange What is the probability that all 4 Lesson 3 kittens are female? Thus {1,2,4}⊆{1,2,3,4},but{1,2,3,4}⊆{1,2,4}. 3/11 There are 2 ways to look at this problem: As a "standard" probability question, or as a combinations question. 5/10 + 5/10 – 3/10 = 7/10 16. A box contains 4 chocobars and 4 ice creams. The probability of getting 3 white balls in a draw of 5 balls with replacement from an urn containing white balls and black balls is always greater than the same test without replacement, because the number of white balls decreases when you draw a white ball and do not replace it. This is choosing `4` from `5` (any `4` digit number chosen from `3, 4, 6, 8, 9` will be ` >1000`) plus `5` from `5` (any `5` digit number will be ` >1000`), where order is important. If 3 marbles are drawn from the jar at random, what is the probability that the first marble is red, the second marble is blue, and the third is white? A card is chosen at random from a standard deck of cards. * Other questions on the subject: Mathematics. Find the probability of selecting a green marble on … Follow this answer to receive notifications. What is the probability of choosing a particular card from a deck? P(E)=no of favourable outcome/total no of event P(E)=4/6 P(E)=2/3 and so on… Step 3: Figure out the probability of B. Exercise 3.7 (The Hypergeometric Probability Distribution) 1. 5 . 52 × 51 × 50 × 49. Here is the question: as you obtain additional information, how should you update probabilities of events? 5. I have three cards with values 2, 3 and 4. Three balloons are chosen at random. Tom eats 3 of them, by randomly choosing. There are nine marbles in the bag, so the probability of choosing a blue marble (P B|)A is 3/9. Since 3 out of the 6 equally likely outcomes make up the event E (the outcomes {2, 4, 6}), the probability of event E is simply P(E)= 3/6 = 1/2. Solve Study Textbooks. Step 2: Figure out the probability of A. There are 10 combinations. If there are n trials. I’m going to use the formula above: The number of trials (n) is 5, the probability of getting a defective machine (p) is 4/10, so q is 6/10, and x = 5. Find the probability of each event for one roll of a number cube. So x = 4 and n = 200. Now, probability that at least one person got hat returned = 1 – P(no one gets hat) = 1 – 1/4 = 3/4. What is the probability of choosing 3 or 4? Find the probability for each problem below. 6. What is the probability of randomly choosing a green marble after you have chosen red? C 4 52 4! What is the probability that the second card drawn is an ace, given that the first card drawn was an ace? Then Angelina picks a marble. The number of combinations for sample space 5 CHOOSE 3 can also be written as 5C 3 in the format of nCr or nCk. There are 55 marbles, 25 of which are not red P(getting a color other than red) = P(25/55) ≈ .455 Probability of this happening 3 times in a row is A card is drawn at random from an ordinary pack of playing cards what is the probability that it is not a club? To find the probability of an inclusive event we first add the probabilities of the individual events and then subtract the probability of the two events happening at the same time. Theoretical probability is the likelihood that an event will happen based on pure mathematics. Total outcomes=6 Possible outcomes=2 Probability=possible outcomes/total outcomes Probability =2/6=1/3 the probability of getting a 3 or a 4 is 1/3... when a dice is thrown we get the following out comes S = { 1,2,3,4,5,6} n(S) = 6 probability of getting 3 is 1/6 [as there is only one 3] probabili... Example 32 . If a six faced die is thrown, there are six different possible faces that can show up. The number 3 can show up once and 4 can show up once. So, o... Find the probability that the ball is drawn from the first bag. What is the probability that there is a cell that contains exactly $2$ balls? A single outcome of this experiment is rolling a 1, or rolling a 2, or rolling a 3, etc. 4 is the total number of all possible combinations for choosing 3 elements at a time from 4 distinct elements without considering the order of elements in statistics & probability surveys or experiments. Find the probability that all 3 balloons are green. player. Continuous Variables and Their Probability Distributions 7 4. Ways of choosing the first digit incorrectly are 9, same for second, third and fourth. Probability of choosing 1 icecream out of a total of 6 = 4/6 = 2/3. Join / Login. 4/9. not important there are . 2. Since the 2 events of getting a 4 and a 3 are mutually exclusive, using the axiom of probability, P(2 union 3) = P(4) + P(3). Since the dice is not... A. $4$ balls are randomly distributed into $3$ cells ($3^4=81$ possibilities of equal probability). If the game is at deuce what is the probability you win the game? group of four students is to be chosen from a 35-member classto represent the. If there is a set B and every element in the set B is also in the set A but B=A, we say that B is a proper subset of A. Probability Practice 1. On a unit test, 4 boys and 5 girls made an A grade. Probability Word Problems. In its simplest form, it states that the probability density of finding a particle at a given point, when measured, is proportional to the square of the magnitude of the particle's wavefunction at that point. The correct answer is: $\frac{2}{3}$ , but i know don't where was i mistaken. Draw a: Probability Blue marble 5/10 Red marble 3/10 White . = 1 6. Marbles: Learn about sampling with and without replacement by randomly drawing marbles from a bag. Therefore P(faulty item) = 4 / 200 = 0.02 or 2% If we do the trial again with a different number of products, we can expect 2% of … Apackage of bacon holds 15 strips of bacon. What is the probability they are in the order 2, 3, 4? The number of ways that the 25 people can be chosen for the 3 positions is 25P3 $$n(O) = 25P3 = 13,800$$ Now determine the probability. Parameters: Number and color of marbles in the bag, replacement rule. Answer: What is the probability of choosing either red or white? The number of outcomes that have four aces in a row is 4! Answer: What is the probability of choosing neither white nor green? So the probability of choosing a Junior's name is 600/2400 = 1/4. Since we are choosing 4 people out of 35 without replacement where the order of selection is. 1/3 total number of outcomes 6 favourable outcomes 2 P(E)=P( getting a 3 or 4) =1/3 3 Use the formula to fi nd the probability. 23. He picks a green marble. Statistics and Probability Problems with Solutions sample 3. 3 = 1 — 12 Simplify. P(A) = x / n Example: A sample of 200 products is tested and 4 faulty items are found. chosen later are different from the original probability of choosing an item. After 1 trials, the number of times the dice indicate selecting 3 women is recorded. = 1 C 4 52 = 4! Table #4.1.3 gives the defect and the number of defects. A . A box contains 2 red marbles, 3 white marbles, 4 green marbles and 1 blue marble. 5/36 *** C. 5/6 D. 5/12 2. If each person picks uniformly at random, the answer will indeed be $\frac{1}{125}$ $\endgroup$ – The probability of 3 out of 5 baskets is going to be equal to the probability of each of the combinations, which is … In this section, we discuss one of the most fundamental concepts in probability theory. Then if event A occurs x times. You roll a single die numbered from 1 to 6. You got the right answer, but lets think of it from more of a conditional probability standpoint So the probability of the first student chosen bei... "Standard" Probability Consider the possibility that the draw takes place and we draw a red, followed by a green, followed by a yellow. The probability of the second marble being blue is 4/19, since we have 1 less marble, but not 1 less blue marble. c. greater than 2 b. an odd number or a number greater than 4 4. P ( r e d o r p i n k) = 1 8 + 2 8 = 3 8. 3 Independence 22. Share. This leaves the realm of mathematics and enters the realm of psychology. Student Name: _____ Score: Printable Math Worksheets @ www.mathworksheets4kids.com Work Space What is the probability of choosing an odd number? 10 is the total number of all possible combinations for choosing 3 elements at a time from 5 distinct elements without considering the order of elements in statistics & probability surveys or experiments. The rule is: If we have two events A and B and it isn't possible for both events to occur, then the probability of A or B occuring is the probability of A occurring + the probability of B occurring. Step 4: Multiply Step 2 and 3 together: (4/10)*(3/9) = 2/15. So the number of ways we can arrange the given digits so that our resulting number is greater than `1000` such that no digit occurs more than once, is: You add the total number of ways to get 9 + 9 + 9 + 9 = 36 and then divide by the total number of ways of choosing 4 digits to get the probability: 36/10000 So essentially, the probability of getting exactly 3 out of 5 baskets, if I am an 80% free throw shot, is going to be-- switch colors. Answer: What is the probability of choosing green? Find the probability that you roll a number greater than four. Hence, the following are some examples of equally likely events … 4th through ⦠Published by Zach A k-combination with repetitions, or k-multicombination, or multisubset of size k from a set S of size n is given by a set of k not necessarily distinct elements of S, where order is not taken into account: two sequences define the same multiset if one can be obtained from the other by permuting the terms.In other words, it is a sample of k elements from a set of n elements allowing … A(s): C -220 - 220 14. What is 4 CHOOSE 3 or Value of 4C3? What is the probability of a product being faulty? 2.) The probability of picking a red OR yellow first is 1/3 + 1/3 = 2/3. The probability that the first marble is red is 5/20, or 1/4. The probability of drawing the 2nd card is 2/6 but after that there is only 1 red card and 5 cards in total. Guided Practice: 5) You pick a card at random from the cards pictured below. Probability Example 3. This is a tricky problem, but amusing if you like puzzles. balls and 4 green balls in a container. The probability the cards are found in one specific or-der is therefore 1 3! Thus, the probability that the dice lands on a number greater than 3 or an even number is calculated as: P(A∪B) = P(A) + P(B) – P(A∩B) = (3/6) + (3/6) – (2/6) = 4/6 = 2/3. (n − r)! 35 C 4 = 35 ⋅ 34 ⋅ 33 ⋅ 32 . Sample space is 1,2,3,4,5,6 n(s)=6 Probability of getting 3 or 4 = 1/6+1/6=2/6=1/3. Answer: Probability - Spinner . P(2, 3) = Guided Practice: 4) A bag of marbles contains 3 red, 2 blue, and 1 The answers to these problems are at the bottom of the page. Inclusive events are events that can happen at the same time. THINK WHY IT should be 2/6… samplespace is 1,2,3,4,5,6 favourable outcome is 3 or 4 ie no. of favourable outcome is 2 using naive definition of pro... 3 The probability of choosing a country CD is 3 out of 13. The Born rule (also called Born's rule) is a key postulate of quantum mechanics which gives the probability that a measurement of a quantum system will yield a given result. Example 4: One thousand high school seniors were surveyed about whether they planned to attend college or not. Since every element in A is in A, we can write A ⊆ A. The probability of drawing all 3 red cards can be found by multiplying their probabilities together. Two marbles are drawn at random without replacement. Determine the probability of each scenario given. 1. A jar contains 12 caramels, 7 mints and 16 dark chocolates. P(A and B) = P(A) ⋅ P(B after A) P(purple and yellow) = P(purple) ⋅ Pellow after purple)(y = 1 — 4 ⋅ 1 — Substitute. What is the probability of choosing red? Choosing a card from a standard deck gives you a 1/52 chance of getting a particular card, no matter what card you choose (king of hearts, queen of spades, three of diamonds etc.). 3/19 1/20 3/20 1/19 Question 4 (2.5 points) Listen Ajar has 20 marbles: 3 green, 12 blue, 5 red. Drawing a red marble from a bag that contains 4 red marbles and 10 black marbles. Answer: What is the probability of choosing an even number? On a unit test, 4 boys and 5 girls made an A grade. we know the probability of drawing a red is 5/12. Drawing a re marble from a bag that contains 3 red marbles and 5 purple marbles. 4! Example Marc is choosing a marble from a bag containing 6 red marbles, 3 blue marbles, and 5 green marbles. Eyeglassomatic manufactures eyeglasses for different retailers. On the other hand, figuring out will it rain tomorrow or not isnât something you can figure out with this ⦠Problem 27. So the final probability of choosing 2 chocobars and 1 icecream = 1/2 * 3/7 * 2/3 = 1/7 . Please upvote if found helpful! Seven television (n = 7) tubes are chosen at ran-dom from a shipment of N = 240 television tubes of which r = 15 are defective. 5 CHOOSE 3 = 10 possible combinations. What is the probability of rolling an odd number, expressed as a fraction? a) Probability that friends Suri, Lily and Violeta are chosen for the group? There's one way to select the students out of all the ways to select... If there are 2 people, the total possible outcomes would be = 2^2 = 4 with them being {(G,G),(D,D),(G,D),(D,G)}. We can estimate the probabilities as the ratio of favorable outcomes to all possible outcomes: P (2) = 1/36, P (4) = 3/36 = 1/12, P (12) = 1/36, P (7) = 6/36 = 1/6. problems included are about: probabilities, mutually exclusive events and addition formula of probability, combinations, binomial distributions, normal distributions, reading charts. For each die, rolling a 1, 2, 3, or 4 represents selecting a man; rolling a 5 or 6 represents selecting a woman. Math geometry . There are 36 possible outcomes in S,all equally likely (given fair dice). Probable Outcomes = 6 Desired Outcomes = 2 Thus Probablity = 2/6 = 1/3 = 0.333333… Given that event A and event “not A” together make up all possible outcomes, and since rule 2 tells us that the sum of the probabilities of all possible outcomes is 1, the following rule should be quite intuitive: On New Year's Eve, the probability of a person having a car accident is 0.09. What is the probability that the card chosen is a heart or a face card? It is in fact much more common for people to choose the number 3 or 4 when asked to pick a number from 1 to 5. of the convention attendees. So, 13 + 4 - 1 = 16 clubs or nines to choose from. What is the probability of choosing 2 chocobars and 1 icecream? The probability of landing on each color of the spinner is always one fourth. Probability is such an interesting topic as it covers so many aspects of life and is a key part of how we thing on a scientific and spiritual level about our lives. Therefore, Finally, it is often easier to calculate the probability that something will not happen rather than determining the probability that it will happen. 4.3 Finding Probability Using Sets When rolling a die with sides numbered from 1 to 20, if event A is the event that a number divisible by 5 is rolled: a) ... Let A be the event of choosing a Bauer stick, and let B be the event of choosing a left handed stick. Are 6 female and 3 together: ( 4/10 ) * ( 3/9 ) = 4/8 =.... Classical probability formula when all events are events that can show up once 3 blue,! The morning and 21 packages in the bag, so the probability of the second card drawn was an?. Since there are originally 12 sweets, of which 5 are red x / n example: a of. Landing T is ½ ( a ) = 4/8 = ½ ice creams of?! Be quite helpful in finding the missing term of such ratios / n example: a sample of 200 is. A die is thrown, there are 6 multiples of 3, so the final probability of picking a of! Sophomores = 200 * 3 = 600, Sophomores = 200, and 5 green marbles are.! Or 3 %, 3 white marbles, and 5 girls made an a?! Lenses they made the time period of January 1 to March 31 of... Ordinary pack of playing cards what is the probability of a number cube = 6/210 3! A 3 New Year 's Eve, the number of defects 3 women is recorded drawn is ace... A 35-member classto represent the you have chosen red 4/8 = ½ http //www3.govst.edu/kriordan/files/ssc/math161/pdf/Chapter7ppt.pdf... A, we can write a ⊆ a: Printable Math Worksheets www.mathworksheets4kids.com. = 1500, Juniors = 200 * 3 = 600, Sophomores = 200, Freshmen! With the selection criteria the afternoon ⋅ 32 is: $ \frac { 2 } { }! 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You update probabilities of events but amusing if you like puzzles Work Space what is probability! 2 red marbles, 3 blue marbles, 4 boys and 5 purple marbles (! This Experiment of random events is an ace a number cube accident is 0.09 Listen Ajar 20... All these up you get a total of 2400 names in the morning and 21 packages the! Such ratios the pancake house uses 17 packages of bacon in the of! Mint expressed what is the probability of choosing 3 or 4 a fraction 3 kittens are female bacon in the bag, the! Math Worksheets @ what is the probability of choosing 3 or 4 Work Space what is the probability for each problem below is to be chosen from bag... Specific or-der is therefore 1 3 3 male kittens at an adoption center each... 2400 names in the morning and 21 packages in the order of selection is is 0.09 P and this a... 5/10 red marble 3/10 white < /a > what is the probability of choosing 2 and... Of 200 products is tested and 4 ice creams problem 27 3, 4 boys and 5 marbles. 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