Question 258127
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
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the probabiltiy that at least one has tree pollen allergy: 1-.0859=.9141
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the probability that 5 have tree pollen allergy: nCr=11C5=462 the coefficient.
462*n^6t^5=462*.8^6*.2^5=.0388
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the probability that 7 have tree pollen: 11C7=330 coefficient
330*n^4t^7=330*.8^4*.2^7=.0017
.
Ed