Question

A retail shop accepts only cash or checks. Suppose that 60% of its customers carry cash, 59% carry checks, and 77% carry cash or checks (or both). What is the probability that a randomly chosen customer at the shop is carrying both cash and checks?

Answer 1

$p(c) = 0.6 \\ p(ch) = 0.59 \\ p(any)= 0.77$

$p(both) = p(c) + p(ch) - p(any) \\ p(both) = 0.6 + 0.59 - 0.77 \\ p(both) = 0.42$