Answer to Question #154281 in Statistics and Probability for Gayani

Question

The American Red Cross says that about 25% of the population has Type B blood. A blood drive is being held at your institute. Suppose that you have selected 20 blood donors in a random way. The probability that exactly 2 of the blood donors have Type B blood is

Answer 1

Given: p = 0.25; x = 2; n = 20

$b(n,p,x) = \binom{n}{x}*p^x* {\lparen1-p\rparen}^{\lparen n-x\rparen}$

Here $\binom{n}{x}\equiv C^x_n = \frac{n!}{x!(n-x)!}$

Then $b(20,0.25,2) = \frac{20!}{2!(20-2)!}*0.25^2*(1-0.25)^{20-2} =$

$= \frac{19*20}{2}*0.0625*0.75^{18} \approx 190*0.625* 0.0056377 \approx 0.066947$

Answer $b \approx 0.066947$