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?
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Expert's answer
2012-02-02T10:56:16-0500
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.
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