Among uses of automated teller machines (atms), 92% use atms to withdraw cash and 29% use them to check their account balance. suppose that 95% use atms to either withdraw cash or check their account balance (or both). given a woman who uses an atm to check her account balance, what the probability that she also uses an atm to get cash? the probability is nothing.

Step-by-step explanation:

Data given

Lets define the following events

A: An user use ATMs to withdraw cash

B: An user use ATMs to check their account balance

92% use ATMs to withdraw cash

29% use them to check their account balance

95% use ATMs to either withdraw cash or check their account balance (or both)

For this case we have some probabilities given:

P(A) =0.92, P(B) =0.29 and P(A U B)=0.95

Solution to the problem

On this case we want to find this probability:

P(A|B) the conditional probability.

By defintion of conditional probability we know that:

In order to find P(A and B) we can use the total probability rule given by:

P(A U B) =P(A)+ P(B) -P(A and B)

And solving for P(A and B) we got:

P(A and B) =P(A) +P(B) -P(AUB) =0.92+0.29-0.95=0.26

And now we can replace in the conditional formula like this:

And then, given a woman who uses an ATM to check her account balance, what the probability that she also uses an ATM to get cash the probability is 0.897

not sure but it may be b, as i said i'm not sure.