Answer:
The required probability = 0.2637
Step-by-step explanation:
Let X represents the no of customers that uses the express checkout.
[tex]X \sim Binomial (n =5, p= 0.25)[/tex]
The probability mass function is given by:
[tex]P(X =x) = \dfrac{5!}{x!(5-x)!}(0.25)^x (1-0.25)^{5-x} \ \ ; for \ x =0,1,2,3,4,5[/tex]
To find:
[tex]P(X =2) = \dfrac{5!}{2!(5-2)!}(0.25)^2 (1-0.25)^{5-2} \ \[/tex]
[tex]P(X =2) = \dfrac{5!}{2!(3)!}(0.25)^2 (0.75)^{3} \ \[/tex]
[tex]P(X =2) = \dfrac{5\times 4 \times 3!}{2!(3)!}(0.25)^2 (0.75)^{3}[/tex]
[tex]P(X =2) = \dfrac{20}{2!}(0.25)^2 (0.75)^{3}[/tex]
P(X = 2) = 0.2637
Thus, the required probability = 0.2637
