1 a b c d e 2 a b 3 Task 1: It's all in the cards. (5 marks total) A card is drawn from a standard deck of 52 playing cards. Leave answers as fractions in lowest terms and odds as a ratio in lowest terms. Find each of the following probabilities or odds: the probability that the card is a diamond (1 mark) the probability that the card is an odd-numbered card (1 mark) the probability that the card is a face card (1 mark) the probability that the card is not a face card (1 mark) the odds in favour of drawing a face card (1 mark) Task 2: To be mutually exclusive or not to be mutually exclusive - that is the question (6 marks total) For each situation, state whether or not the events are mutually exclusive (and explain why) and determine the probability of the event occurring. Leave answers as fractions in lowest terms. rolling a power of 2 or a multiple of 3 with a single 12-sided die (3 marks) drawing an even-numbered card or a card with a red suit from a standard deck of cards (3 marks) Task 3: What are the chances? (4 marks total) 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)