Question

20% of the patron's order the chef's special. The probability that 2 out of the next ten customers will order the chef's special is

Answer 1

Answer:

$P(x =2) = 0.3020$

Step-by-step explanation:

Given

$p =20\% = 0.20$

$n = 10$

Required

$P(x = 2)$

This question is an illustration of binomial distribution where:

$P(X = x) = ^nC_x * p^x * (1 - p)^{n-x$

So, we have:

$P(x =2) = ^{10}C_2 * 0.20^2 * (1 - 0.20)^{10-2}$

$P(x =2) = ^{10}C_2 * 0.20^2 * 0.80^8$

This gives

$P(x =2) = \frac{10!}{(10 - 2)!2!} * 0.20^2 * 0.80^8$

$P(x =2) = \frac{10!}{8!2!} * 0.20^2 * 0.80^8$

Expand

$P(x =2) = \frac{10*9*8!}{8!2*1} * 0.20^2 * 0.80^8$

$P(x =2) = \frac{10*9}{2} * 0.20^2 * 0.80^8$

$P(x =2) = 45 * 0.20^2 * 0.80^8$

$P(x =2) = 0.3020$