Respuesta :
Answer:
[tex]P(A|B) =\frac{P(A and B)}{P(B)}=\frac{0.26}{0.29}=0.897[/tex]
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:
[tex]P(A|B) =\frac{P(A and B)}{P(B)}[/tex]
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:
[tex]P(A|B) =\frac{P(A and B)}{P(B)}=\frac{0.26}{0.29}=0.897[/tex]
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
