Among uses of automated teller machines ATMs 92 use ATMs to

Among uses of automated teller machines (ATMs), 92% use ATMs to withdraw cash and 32%use them to check their account balances. Suppose that 96% use ATMs to ethier withdraw cash or check their account balance (or both). Given a woman who uses an ATM to checek her account balance, whats the probability that she also uses an ATM to get cash?

Solution

Let

W = withdraw
B = balance inquiry

Thus,

P(W|B) = P(B n W) / P(B)

As

P(B n W) = P(B) + P(W) - P(B U W) = 0.92 + 0.32 - 0.96 = 0.28

Thus,

P(W|B) = 0.28/0.32 = 0.875 [ANSWER]