Question

P(A) = 0.40 P(B) = 0.60 P(A|B) = 0.08 What is P(A and B)?

Answer 1

`P(A \: and \: B) = 0.048`

Explanation:

Recall that the probability of event A , given that event B has occurred is given as:

`P(A|B)=(P(A\cap B))/(P(B))`

Since P(A|B) = 0.08 and P(A) = 0.40 are not the the two events are not independent.

We substitute the probabilities to get:

`0.08=(P(A\cap B))/(0.60)`

`P(A\cap B) = 0.08 * 0.6 = 0.048`

Therefore

`P(A \: and \: B) = 0.048`