Question

Given P(A) = 0.7 and P(B) = 0.8,

A) If A and B are independent events, compute P(A ∩ B).
B) If P(B | A) = 0.9, compute P(A ∩ B).

Answer 1

To compute P(A ∩ B) when A and B are independent events, use the formula P(A) * P(B). For part A, P(A ∩ B) = 0.56 and for part B, P(A ∩ B) = 0.63.

Step-by-step explanation:

To compute P(A ∩ B) when A and B are independent events, we use the formula P(A ∩ B) = P(A) * P(B).

So, for part A, we have P(A) = 0.7 and P(B) = 0.8. Thus, P(A ∩ B) = 0.7 * 0.8 = 0.56.

For part B, the probability P(B | A) = 0.9. To find P(A ∩ B), we use the formula P(A ∩ B) = P(B | A) * P(A).

Substituting the given values, we have P(A ∩ B) = 0.9 * 0.7 = 0.63.