Question

A bank accepts thirty percent of loan requests from farmers. Ten loan requests from framers are randomly selected for consideration by the bank. Find the probability exactly 2 are accepted and more than 3 are accepted.

Answer 1

The probability that exactly 2 are accepted is:

$P(2) = C(10;2)×0.3^2×(1 - 0.3)^8 = 10!/(2!×8!)×0.09×0.7^8 = 0.2335.$

The probability that more than 3 are accepted is:

$P(>3) = 1 - P(0) - P(1) - P(2) - P(3) = 1 - 0.7^10 - 10×0.3×0.7^9 - 45×0.3^2×0.7^8 - 120×0.3^3×0.7^7 = 0.3504.$