Question

Of the volunteers donating blood in a clinic, 80% have the Rhesus (Rh) factor present in their blood. What is the smallest number of volunteers who must be selected if we want to be at least 90% certain that we obtain at least five donors with the Rh factor?

Solution

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Given:

k=5k=5

p=80%=0.80p=80\%=0.80

Definition binomial probability:

P(X=k)=n!k!(nk)!pkqnk=n!k!(nk)!pk(1p)nkP(X=k)=\dfrac{n!}{k!(n-k)!}p^kq^{n-k}=\dfrac{n!}{k!(n-k)!}p^k(1-p)^{n-k}

Add the corresponding probabilities:

P(X5)=P(X=5)+...+P(X=n)P(X\geq 5)=P(X=5)+...+P(X=n)

Evaluate for a few nn values:

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