Let A and B be two independent events such that Then P(B) is equal to

Engineering

Mathematics

Basic Definitions Related to Probability

Question

Let A and B be two independent events such that $P (A) = \frac{1}{5}, P (A \cup B) = \frac{7}{10} .$ Then P(B) is equal to

$\frac{3}{8}$

$\frac{2}{7}$

$\frac{7}{9}$

none of these

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∵ P(A∪B) = P(A) + P(B) − P(A∩B) = P(A) + P(B) − P(A)P(B) since A and B are independent
putting the values
$\frac{7}{10} = \frac{1}{5} + P (B) - (\frac{1}{5} \cdot P (B))$

$P (B) \cdot \frac{8}{10} = \frac{7}{10} - \frac{2}{10} = \frac{5}{10} = \frac{1}{2}$

$P (B) = \frac{1 / 2}{8 / 10} = \frac{1}{2} \cdot \frac{10}{8} = \frac{5}{8}$

$P (\bar{B}) = 1 - P (B) = 1 - \frac{5}{8} = \frac{3}{8}$