Discrete Probability

Question

If it is assumed that 0.08 of males are seniors, what is the probability that there are three seniors in a group of 10 men?

Answer 1

If we let s=seniors and n=non seniors then we can treat this as a binomial expansion of

(s+n)^10 we would be interested din the term s^3n^7 . The coefficient of this term is 10C3 which is (10!)/(10-3)! (3!)= ( 10x9x8)/6 which equals 120

prob senior= .08 so prob of non senior is .92

So probability is 120 (.08)^3 (.92)^7= .034