First slide

Theorems of probability

Question

Let A and B be two events such that $P (A \cap B^{'}) = 0 .20$ $P (A^{'} \cap B) = 0 .15, P (A^{'} \cap B^{'}) = 0 .1,$ then P(A/B) is equal to

Moderate

A

11/14
B

2/11
C

2/7
D

1/7

Solution

$P (A \cap B^{'}) = P (A) - P (A \cap B) = 0 .20$
Also,
$\begin{array}{l} P (A^{'} \cap B) = P (B) - P (A \cap B) = 0 .15 \\ \Rightarrow P (A) + P (B) - 2 P (A - B) = 0 .35 \\ Now, \\ P (A^{'} \cap B^{'}) = 1 - P (A \cup B) \\ \Rightarrow 0 .1 = 1 - P (A) - P (B) + P (A \cap B) \\ \Rightarrow P (A) + P (B) - P (A \cap B) = 0 .9 \\ \Rightarrow P (A \cap B) = 0 .9 - 0 .35 = 0 .55 \\ and P (A) = 0 .75, P (B) = 0 .70 \\ Now, \\ P (A / B) = \frac{P (A \cap B)}{P (B)} = \frac{0 .55}{0 .70} \end{array}$

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