Answer to Question #167724 in Statistics and Probability for aaliyah

Question

1.    At Foodland Supermarket 45% of customers pay by credit card. Find the probability that in a randomly selected sample of fifteen customers.

a.    Exactly four pay by credit card

Answer 1

By condition, the probability that the client will pay with a credit card is

$p = 0.45 \Rightarrow q = 1 - p = 0.55$

Then, according to Bernoulli's formula, the wanted probability is

${P_{15}}\left( 4 \right) = C_{15}^4{p^4}{q^{15 - 4}} = \frac{{15!}}{{4!11!}} \cdot {0.45^4} \cdot {0.55^{11}} = \frac{{12 \cdot 13 \cdot 14 \cdot 15}}{{24}} \cdot {0.45^4} \cdot {0.55^{11}} \approx 0.07798$

Answer: $\approx 0.07798$