Answer to Question #6189 in Statistics and Probability for Debbie

Question

Out of 2 million hay fever sufferers in Canada, 20% are allergic to tree pollen. If 11 hay fever victims are picked at random, what is the probability that t have tree pollen allergy?

Answer 1

Out of 2 million hay fever sufferers in Canada, 20% are allergic to tree pollen. If 11 hay fever victims are picked at random, what is the probability that m have tree pollen allergy?

This is a binomial expansion.
t=tree pollen allergy, n=no tree pollen allergy
Let t=0.2 and n=0.8
(n+t)^11

The probability that m have tree pollen:
the coefficient: C(11,m)=11!/(m!(11-m)!)
P = 11!/(m!(11-m)!)*n^(11-m)*t^m = 11!/(m!(11-m)!)*0.8^(11-m)*0.2^m.