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\"I. A certain town performs a survey and discovers that 15% of their population have hazel-coloured eyes. a. if 5 people are randomly selected from the town, what is the probability that 2 of the people have hazel eyes? b. What is the expected number of people with hazel eyes in the group of 5 people? o. Create a probability histogram for the above situation for the outcomes from 0 to 5 people with hazel eyes. 2. A regular sixsided die and a regular eight-sided die are rolled to form a sum. a. Determine the probability distribution for the sum of the two dicei b. Create a frequency histogram for the probability distribution. c. Determine the expected sum of the two dice. 3. A hockey team has 23 players on it consisting of 13 fonvards, 7 defenseman and 3 goalies. The team charity golf tournament is coming up and 8 players are required to play. a. Determine the probability that 3 defensemen are chosen to play in the golf tournament. b. Determine the probability that at least one goalie will play in the golf tournament. c. What is the expected number of forwards that will play in the golf tournament? 4. A game of chance involves a regular deck of 52 cards. The game costs $3 to play. If you draw an ace. you win $20. if you draw a lace card. you win $5. If you draw a 10, you win $3. If you draw any other card. you lose. a. Caiculate the expected winnings for the player. 1:. Calculate the expected prots for the game owner. 0. Is this game a fair game? If not, explain why the game owner would want the game slightly in his favour? 5. Consider a game in which you roll a regular eight-sided die. When you roll an odd number you win an amount equal to double the roll. When you rol an even number you win an amount equal to half the roll. a. What type of distribution best describes the situation in this game? b. Calculate how much you should charge someone to play your game in order for it to be a fair game