If A and B are independent events with P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B)?

Solution:

Given A and B are independent events

P(A) = 0.5 and P(B) = 0.5

By using the rules of probability, we know that when A and B are independent events then the intersection of them is the product of their individual probability

⇒ P(A ∩ B) = P(A).P(B)

⇒ P(A ∩ B) = 0.5 × 0.5

⇒ P(A ∩ B) = 0.25

Hence, P(A ∩ B) = 0.25

Thus, the probability of events a and b that occurred simultaneously is p(a ∩ b) = 0.25.

If A and B are independent events with P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B)?

Summary:

If A and B are independent events with P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B) = 0.25