Q1 Expected mean Find the mean, p, for a binomial distribution X ~ 5(200, E ). [2] 5 A cricket match is to be played over 4 days. The probability that it will rain on any day is E . Find the expected number of rainy days. [2] 4 E of Karl's shirts are white. Out of 10 shirts picked at random, how many would you expect to be white? [2] Q2 Expected mean, variance and probability The probability that David arrives Dean, the wedding photographer, on time to his maths lesson is 0.7. has 10% chance that his photos are out of focus. He has 6 lessons per week. He takes 400 photos at Sophie's wedding. Find the probability that he arrives on time for Find the mean and variance of the number of photos that are out of focus. (a) all 6 lessons D (to 3 d.p.) [2] mean = [2] (b) 3 out of the 6 lessons. (to 3 d.p.) [2] variance = [2] What is the expected number of lessons he is on time for each week? [2]