SOLUTION: Out of 2 million hay fever sufferers, 20% are allergic to tree pollen. If 11 hay fever victims are picked at random what is the probability that 5 have tree pollen what is the prob
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Question 258127: Out of 2 million hay fever sufferers, 20% are allergic to tree pollen. If 11 hay fever victims are picked at random what is the probability that 5 have tree pollen what is the probability that 7 have tree pollen,what is the probability that none have tree pollen allergy and what is the probabiltiy that at least one has tree pollen allergy? Any help with this would be greatly appreciated.
Thanks Susan Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website! This is a binomial expansion.
t=tree pollen allergy, n=no tree pollen allergy
Let t=.2 and n=.8
(n+t)^11
.
none have tree pollen allergy: n^11=.8^11=.0859
.
the probabiltiy that at least one has tree pollen allergy: 1-.0859=.9141
.
the probability that 5 have tree pollen allergy: nCr=11C5=462 the coefficient.
462*n^6t^5=462*.8^6*.2^5=.0388
.
the probability that 7 have tree pollen: 11C7=330 coefficient
330*n^4t^7=330*.8^4*.2^7=.0017
.
Ed
