Drug users Binomial Distribution problem

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Ten percent of all olympic athletes are tested for drugs at the conclusion of their event. 1% of all athletes use performance enhancing drugs. Of the 1000 Olympic wrestlers competing from all over the world, America sends 10. Find
a. the expected number of American wrestlers who are tested for drugs
b. the probability that half the American wrestlers are tested for drugs
c. the probability that at least two American wrestlers are tested for drugs
d. the expected number of drug users among all wrestlers.

My answers:

a. expected number is = n x p where p = 0.01, so 10 x 0.01 = 1
b. ?
c. ?
d. expected number is = n x p = 0.01 x 1000 = 10
 
Correct on answers a and d


For (b) We know p=0.1, q=0.9, n = 10
We are trying to find half or 5.

\(\displaystyle \large\\10C5(0.1)^5(0.9)^5\\\approx0.0015\)

For (c) We are finding at least 2

\(\displaystyle Pr(X\geq2)=1-Pr(X<2)\)

\(\displaystyle \large\\10C0(0.1)^0(0.9)^{10}+10C1(0.1)(0.9)^9\\\approx0.736\)

Therefore \(\displaystyle \large\\1-0.736=0.264\)
 
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