10. A medical experiment involved 35 men and 30 women of which 25 were randomly selected to take part in testing a new medication. What is the probability that a) 15 were men? b) 15 were women? (five marks)9. A bin contains 8 apples and 12 pears. Five pieces of fruit are randomly chosen from the bin. a) What is the probability that two are apples? b) What is the expected number of apples selected?(five marks)8. Each expression represents the probability of a hypergeometric distribution. State the values of the unknowns. Co Xe Ca 10 Xn1 a b) c) d) 15 10 18 7 C13 (five marks)7 Model each of the following situations using a hypergeometric distribution. Identify the discrete random variable, X, the size of the population, n, the number of successes available, a, and the number of trials, r. a) In a class of 30 students, 18 have a driver's licence. Five students are selected at random and the number with a driver's licence is recorded. MDM4U Lesson Assignment Page 5 b) A 7-card hand is dealt from a standard deck. The number of face cards is recorded.(five marks)6. A bin of 100 travel clocks are tested to see if they work properly, knowing that 5% of them are defective. The clocks are checked until a defective clock is found. a) Explain why this situation cannot be modelled using a binomial distribution. b) Describe how to change this situation so that it can be modelled using a binomial distribution. (five marks) 6. A bag contains six green and nine black marbles. A marble is selected and returned to the bag. This process continues until a marble has been drawn five times. What is the probability that a) four marbles are green? b) four marbles are black? (five marks)5. Model each of the following situations using a binomial distribution. Identify the discrete random variable, X; the number of trials, n; the probability of success, p; and the probability of failure, q, in any trial. a) A game consists of rolling a die eight times. You win if the result is 5 or 6. You record the number of wins. b) A stand of 500 trees is infected by a particular insect. The chance of survival is 30%. The number of surviving trees is recorded.(five marks)