1. The number of red lights, Y , that Sam stops at on his way to work is a random variable with probability distribution given by: y 0 1 2 3 P (Y = y) 0.2 p 0.6p p2 (a) Use definition of probability to show p = 0.4. (3 marks)

(b) Find P (Y > 1|Y 3). (2 marks) (c) Hence, find the mean of Y . (2 marks) 2. For a certain population the probability of a person being born with the specific gene SPGE is 3 5. The probability of a person having this gene is independent of any other person in the population having this gene. (a) In a random selected group of four people, what is the probability that three or more people have the SPGE gene? (b) In a randomly selected group of four people, what is the probability that exactly two people have the SPGE gene, given that atleast one of those people has the SPGE gene?