3 A cooler has 24 Greek yogurt containers and 6 vanilla yogurt containers. The person in charge of distributing the yogurt reaches into the cooler (without looking) and randomly picks them out of the cooler. What is the probability that your friend gets a Greek yogurt and that you get a vanilla yogurt? Leave answers as percentages rounded to one decimal place. (4 marks) a b Task 4: Tetrahedral sums (7 marks total) Two 4-sided dice are tossed and the sum of the down sides noted. A 4-sided die doesn't have an \"up\" face like a 6-sided die has, so the down side is used. Create a probability distribution (3 marks) and graph (1 mark) for this experiment. Determine the expected value of the sum. (3 marks) a b c Task 5: Probability distributions with dice (4 marks total) Two 4-sided dice are tossed 10 times. Leave probability answers as percents rounded to one decimal place. Is this a binomial or a hypergeometric distribution? Explain. (1 mark) What is the probability that a sum of 4 occurs, at most, twice? (2 marks) Calculate the expected number of times that a sum of 3 should occur. (1 mark) 4 5 6 a b c Task 6: Probability distributions with socks (4 marks total) A drawer contains 5 pairs of green socks, 3 pairs of black socks, and 4 pairs of red socks. All of the pairs are together, meaning that there are not 24 randomly distributed socks, but 12 pairs. You reach into the drawer and pull out 3 pairs of socks without putting any back. Is this a binomial or a hypergeometric distribution? Explain. (1 mark) What is the probability that you get 2 pairs of green socks? Leave your answer as a fraction in lowest terms. (2 marks) What is the expected number of pairs of green socks? (1 mark) Q 3: A cooler has 24 Greek yogurt containers and 6 vanilla yogurt containers. The person in charge of distribu Probability Q4. Two 4-sided dice are tossed and the sum of the down sides noted. A 4-sided die doesn't have an \"up\" face like a 6-sided Create a probability distribution (3 marks) and graph (1 mark) for this experimen Outcome 2 3 4 5 6 7 8 0.30 0.25 14.5 435 0.20 0.15 0.10 0.05 0.00 1 Determine the expected value of the sum. (3 marks) Expected Value Q5.Two 4-sided dice are tossed 10 times. Leave probability answers as percent rounded to one decimal place. 2 A) Is this a binomial or a hypergeometric distributi Binomial distribution, becau B) What is the probability that a sum of 4 occurs, at most, twic P(a sum of 4 occur) P(a sum of 4 does not occur) Probability = P(a sum of 4 never occur) + P(a su = (13/16)^10 + 10C1 * (3/16) * (13/16)^9 + 10 71.5% C) Calculate the expected number of times that a sum of 3 shou P(a sum of 3 occur) Expected number of times 6.A drawer contains 5 pairs of green socks, 3 pairs of black socks, and 4 pairs of red socks. All of the pairs are together, m a Is this a binomial or a hypergeometric distribution? Exp Hypergeometric distribution b. What is the probability that you get 2 pairs of green socks? L Probability c)What is the expected number of pairs of green socks? (1 mar Expected number of pairs rson in charge of distributing the yogurt reaches into the cooler (without looking) and randomly picks them out of the co Probability = 24C1*6C1/30C2 = 24*6/435 = 33.1% 33.1% ve an \"up\" face like a 6-sided die has, so the down side is used. 1 mark) for this experiment Number of possible outcome (1,1) 1 (1,2) (2,1) 2 (1,3) (2,2) (3,1) 3 (1,4) (2,3) (3,2) (4,1) 4 (2,4) (3,3) (4,2) 3 (3,4) (4,3) 2 (4,4) 1 Probability 0.06 0.125 0.1875 0.25 0.1875 0.125 0.0625 Probability 0.30 0.25 0.20 0.15 0.10 0.05 0.00 1 2 3 4 5 the sum. (3 marks) e decimal place. 5 6 7 a hypergeometric distribution? Explain. (1 mark) Binomial distribution, because the trials are independent of each other. of 4 occurs, at most, twice? (2 marks) 0.1875 0.8125 um of 4 never occur) + P(a sum of 4 occurs once) + P(a sum of 4 occurs twice) C1 * (3/16) * (13/16)^9 + 10C2 * (3/16)^2 * (13/16)^8 times that a sum of 3 should occur. (1 mark) 0.125 1.25 times All of the pairs are together, meaning that there are not 24 randomly distributed socks, but 12 pairs. You reach into the drawer and pull o ergeometric distribution? Explain. (1 mark) Hypergeometric distribution, because the results of each trials are dependent. t 2 pairs of green socks? Leave your answer as a fraction in lowest terms. (2 marks 0.3181818182 irs of green socks? (1 mark) number of pairs 1.25 picks them out of the cooler. What is the probability that your friend gets a Greek yogurt and that you get a vanilla yogu h into the drawer and pull out 3 pairs of socks without putting any back. that you get a vanilla yogurt? Leave answers as percentages rounded to one decimal place. (4 marks