First slide

Theorems of probability

Question

Let A and B arc events of an experiment and $P (A) = 1 / 4$ , $P (A \cup B) = 1 / 2$ , then value of $P (B / A^{c})$ is

Moderate

A

2/3
B

1/3
C

5/6
D

1/2

Solution

$\begin{array}{l} P (A) = \frac{1}{4}, P (A \cup B) = \frac{1}{2} \\ P (\frac{B}{A^{C}}) = \frac{P (B \cap A^{C})}{P (A^{C})} \\ = \frac{P (A \cup B) - P (A)}{1 - P (A)} \\ [∵ P (A \cup B) + P (B) - P (A \cap B)] \\ = \frac{\frac{1}{2} - \frac{1}{4}}{1 - \frac{1}{4}} = \frac{1}{4} \times \frac{4}{3} = \frac{1}{3} \end{array}$

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