1. Tardigrade
  2. Question
  3. Mathematics
  4. Let A and B be independent events with P(A) = 1/4 and P(A ∪ B) = 2P(B) - P(A). Find P(B)

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $A$ and $B$ be independent events with $P(A) = 1/4$ and $P(A \cup B) = 2P(B) - P(A)$. Find $P(B)$

Probability - Part 2

Solution:

We know that,
$P(A \cup B ) = P(A) + P(B) - P(A \cap B)$
$= P(A) + P(B) - P(A) \,P(B)$
(Since $A$, $B$ are independent)
Thus, we know that
$1/4 + P(B) - (1/4)\, P(B) = 2P(B) - 1/4$, implying that $P(B) = 2/5$.