Question

Suppose P(A or B)= 2/3 and P(A)= 1/4. Assume A and B are independent events. Find P(B)
Hint: A and B are NOT disjoint.

Answer 1

Answer on Question #39752 - Math - Statistics

Question: Suppose $P(A \text{ or } B) = 2/3$ and $P(A) = 1/4$. Assume A and B are independent events. Find P(B). Hint: A and B are NOT disjoint.

Solution: $2/3 = P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) = [A \text{ and } B \text{ are independent, so } P(A \text{ and } B) = P(A)P(B)] = P(A) + P(B) - P(A)P(B) = 1/4 + P(B) - (1/4)P(B) = 1/4 + (3/4)P(B)$.

Then $P(B) = (2/3 - 1/4) * (4/3) = (5/12) * (4/3) = 5/9$.

Answer: $P(B) = 5/9$.