. A certain town performs a survey and discovers that 15% at their population have hazel-coloured eyes. a If 5 people are randomly selected tram the town. whet Is the probability that 2 01 the people have hazel eyes? bi What is the expected number of people with hazel eyes In the group at 5 people? c Create a probability histogram for the above situation tor the outcomes [rum 0 to 5 people with hazel eyes, 2. A regular Six-sided die and a regular eight-sided die are rolled to term a sum 3. Determine the probability distribution for the sum of the two diner 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 la forwards, T delensernan and 3 goalies\" The team charity golf tournament is coming up and B players are required to play 3 Determine the probability that 3 delensemen are chosen to play in the goll toumamenl. b Determine the probability that at least one goalie wrll play in the golt tournament' 6 What is the expected number of lorwards that will play in the goil tournament? 4. A game of chance involves a regular deck ol 52 cards. The game costs $3 to play, It you draw an ace. you win 520 it 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. Calculate the expected winnings for the player. in Calculate the expected prots for the game owner. C Is this game a fair game? If not. explain why the game owner would want the game slightly in his layout? 5. Consrder 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 roll an even number you wrn an amount equal to half the roll. a What type of distribution best describes the situation in this game? be Calculate how much you should charge someone to play your game in order for it to be a fair game. /