Question

About 1/4 of all adults in the United States have type O+ blood. If three randomly selected adults donate blood, find the probability of each of the following events. (Round your answers to four decimal places.) (a) All three are type O+. 0.0156 Correct: Your answer is correct. (b) None of them is type O+. 0.4219 Correct: Your answer is correct. (c) Two out of the three are type O+.

Answer 1

Answer:

a) 0.0156

b) 0.4219

c) 0.1406

Step-by-step explanation:

We are given the following information:

We treat adult having type O+ blood as a success.

P(Adult have type O+ blood) = 0.25

Then the number of adults follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 3

a) All three are type O+

$P(x =3)\\= \binom{3}{3}(0.25)^3(1-0.25)^0\\= 0.0156$

b) None of them is type O+

$P(x =0)\\= \binom{3}{0}(0.25)^0(1-0.25)^3\\= 0.4219$

c) Two out of the three are type O

$P(x =2)\\= \binom{3}{2}(0.25)^2(1-0.25)^1\\= 0.1406$