# Answer to Question #6189 in Statistics and Probability for Debbie

Question #6189

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?

Expert's answer

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.

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.

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