Let A and B be two events such that P(A) = 1/2, P(B) = p and P(A ∪ B) = 3/5, find ‘p’ if A and B are independent events.

For independent events P(A ∩ B) = P(A)P(B) = p/2. P(A ∪ B) = P(A) + P(B) - P(A ∩ B) 3/5 = 1/2 + p - p/2 = 1/2 + p/2 p/2 = 3/5 - 1/2 = 1/(10) 1/5

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Solve the following.

Let A and B be two events such that P(A) = 1/2, P(B) = p and P(A ∪ B) = 3/5, find ‘p’ if A and B…

Let $A$ and $B$ be two events such that $P(A) = \frac{1}{2}$, $P(B) = p$ and $P(A \cup B) = \frac{3}{5}$, find ‘$p$’ if $A$ and $B$ are independent events.

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Answer

For independent events $P(A \cap B) = P(A)P(B) = \frac{p}{2}$. $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ $\frac{3}{5} = \frac{1}{2} + p - \frac{p}{2} = \frac{1}{2} + \frac{p}{2}$ $\frac{p}{2} = \frac{3}{5} - \frac{1}{2} = \frac{1}{10}$

Final answer: $\frac{1}{5}$