N2007 P2 Q6

In a large population, 24% have a particular gene, A, and 0.3% have gene B. Find the probability that, in a random sample of 10 people from the population, at most 4 have gene A.[2]

A random sample of 1000 people is taken from the population. Using appropriate approximations, find

1. the probability that between 230 and 260 inclusive have gene A,[3]
2. the probability that at least 2 but fewer than 5 have gene B.[2]