Question

Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram.P(A)=0.41P(B)=0.34 and P(AandB)=0.25 P(B∣notA)=

Answer 1

So to solve this question let's use the following table:

In this case

$\bar{A}$

is not A

and

$A\cap B$

is AandB

So let's apply as the first step number 5 of the table

$P(B|\bar{A})=\frac{P(B\cap\bar{A})}{P(\bar{A})}$

Now for the numerator let's apply 3 and for the denominator apply 1

$\frac{P(B\operatorname{\cap}\bar{A})}{P(\bar{A})}=\frac{P(B)-P(B\cap A)}{1-P(A)}$

And we replace the probabilities

$\frac{0.34-0.25}{1-0.41}=\frac{0.09}{0.59}=0.15$

Answer: P(B∣notA)=0.15