If A and B are two independent events such that and , then

Engineering

Mathematics

Conditional Probability

Question

If A and B are two independent events such that $P (A) = \frac{1}{3}$ and $P (B) = \frac{3}{4}$ , then $p {\frac{B}{(A \cup B)}}$

$\frac{7}{10}$

$\frac{8}{10}$

$\frac{9}{10}$

$\frac{6}{10}$

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Given, $P (A) = \frac{1}{3}, P (B) = \frac{3}{4}$

we know the for 2 independent events A, B

P(A⋂B) = P(A) x P(B)

$= \frac{1}{3} \times \frac{3}{4}$

$= \frac{1}{4}$

P(AUB) = P(A) + P(B) – P(A⋂B)

$= \frac{1}{3} + \frac{3}{4} - \frac{1}{4}$

$= \frac{1}{3} + \frac{1}{2}$

$= \frac{5}{6}$

$P \{\frac{B}{(A \cup B)}\} = \frac{3 / 4}{5 / 6}$

$= \frac{3}{4} \times \frac{6}{5}$

$= \frac{9}{10}$

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