First slide

Theorems of probability

Question

A and B are two candidates seeking admission in IIT. The probability that A is selected is 0.5 and the probability that both A and B are selected is at most 0.3.The probability of B getting selected cannot exceed.

NA

Solution

$Given P (A) = 0.5 and P (A \cap B) \leq 0.3$

$we have P (A \cup B) = P (A) + P (B) - P (A \cap B) \leq 1$
$\Rightarrow P (A) + P (B) \leq 1 + P (A \cap B) \leq 1 + 0.3 = 1.3$
$\Rightarrow 0.5 + P (B) \leq 1.3 \Rightarrow P (B) \leq 0.8$
Thus probability of B getting selected cannot exceed 0.8

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