Question

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

Answer 1

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)=(P(B\cap A))/(P(A))\\\\\\\Rightarrow P(B/A)=(P(A\cap B))/(P(A))\\\\\\\Rightarrow P(B/A)=(0.20)/(0.50)\\\\\\\Rightarrow P(B/A)=0.40.`

Thus, P(B/A) = 0.40.

Answer 2

0.4

Explanation:

Use the formula for conditional probability.

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