Question

P(A) = 0.50 P(B)= 0.80 P(A and B) = 0.20 . what is P(B\A)?

Answer 1

Answer:

0.4

Step-by-step explanation:

Use the formula for conditional probability.

P(B|A) = P(A&B)/P(A) = 0.20/0.50 = 0.4

Answer 2

Answer:  P(B/A) = 0.40.

Step-by-step explanation:  For any two events A and B, given that

$P(A)=0.50,~~P(B)=0.80,~~P(A\cap B)=0.20.$

We are to find the conditional probability of happening of event B given event A has already happened.

That is,

$P(B/A)=?$

From the formula for conditional probability, we have

$P(B/A)=\dfrac{P(B\cap A)}{P(A)}\\\\\\\Rightarrow P(B/A)=\dfrac{P(A\cap B)}{P(A)}\\\\\\\Rightarrow P(B/A)=\dfrac{0.20}{0.50}\\\\\\\Rightarrow P(B/A)=0.40.$

Thus, P(B/A) = 0.40.