Question

Twenty-five percent of the customers entering a grocery store between 5 P.M. and 7 P.M. use an express checkout. Consider five randomly selected customers, and let x denote the number among the five who use the express checkout. Find the probability that 2 of the customers use the express checkout.

Answer 1

Answer:

The required probability = 0.2637

Step-by-step explanation:

Let X represents the no of customers that uses the express checkout.

$X \sim Binomial (n =5, p= 0.25)$

The probability mass function is given by:

$P(X =x) = \dfrac{5!}{x!(5-x)!}(0.25)^x (1-0.25)^{5-x} \ \ ; for \ x =0,1,2,3,4,5$

To find:

$P(X =2) = \dfrac{5!}{2!(5-2)!}(0.25)^2 (1-0.25)^{5-2}$

$P(X =2) = \dfrac{5!}{2!(3)!}(0.25)^2 (0.75)^{3}$

$P(X =2) = \dfrac{5\times 4 \times 3!}{2!(3)!}(0.25)^2 (0.75)^{3}$

$P(X =2) = \dfrac{20}{2!}(0.25)^2 (0.75)^{3}$

P(X = 2) = 0.2637

Thus, the required probability = 0.2637