Answer to Question #228036 in Statistics and Probability for Nick

Question

Probability of a customer making a purchase is 0.7. Four customers walk into the store. What is the probability that two of the four customers will not make a purchase?

Answer 1

$P(X=x) = C^n_xp^x(1-p)^{n-x} \\ p=0.7 \\ n= 4$

Let X= number of customers making a purchase.

$P(X=2) = C^4_2 \times 0.7^2 \times (1-0.7)^{4-2} \\ = \frac{4!}{2!(4-2)!} \times 0.49 \times 0.09 \\ = 6 \times 0.49 \times 0.09 \\ = 0.2646 \\ = 26.46 \; \%$

The probability that two of the four customers will not make a purchase is 26.46 %.