Events A and B are such that $P(A) = \frac{1}{3}$, $P(B) = \frac{1}{2}$ and $P(A \cup B) = \frac{2}{3}$. Find $P(A \cap B)$.

Question

Accepted Answer

$\frac{1}{6}$. Using the addition rule: P(A ∪ B) = P(A) + P(B) − P(A ∩ B). Substituting: 2/3 = 1/3 + 1/2 − P(A ∩ B). Therefore P(A ∩ B) = 1/3 + 1/2 − 2/3 = 2/6 + 3/6 − 4/6 = 1/6.

Answer

A) $\frac{1}{6}$

Answer

B) $\frac{1}{4}$

Answer

C) $\frac{5}{6}$

Answer

D) $\frac{1}{3}$

Events A and B are such that $P(A) = \frac{1}{3}$, $P(B) = \frac{1}{2}$ and $P(A \cup B) = \frac{2}{3}$. Find $P(A \cap B)$.

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