Question

Given P(A) = 0.3, P(B) 0.63 and P(BA) = 0.79, find the value of

P(A and B), rounding to the nearest thousandth, if necessary.

Answer 1

P(A and B) = 0.14.

Explanation:

Venn probabilities:

Suppose we have two events, A and B. The probability P(A and B) is given by:

`P(A \cap B) = P(A) + P(B) - P(A \cup B)`

In which
`P(A \cup B)` is P(A or B).

In this question:

P(A) = 0.3, P(B) = 0.63, P(A or B) = 0.79. So

`P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.3 + 0.63 - 0.79 = 0.93 - 0.79 = 0.14`

So

P(A and B) = 0.14.