Probability Ques 36
$A$ 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 atmost $0.3$ . Is it possible that the probability of $B$ getting selected is $0.9 ?$
(1982, 2M)
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Answer:
Correct Answer: 36.(No)
Solution:
- Given, $P(A)=0.5$ and $P(A \cap B) \leq 0.3$
$\Rightarrow P(A)+P(B)-P(A \cup B) \leq 0.3 $
$\Rightarrow P(B) \leq 0.3+P(A \cup B)-P(A) \leq P(A \cup B)-0.2 $
$\therefore {[\text { since, } P(A \cup B) \leq 1 \Rightarrow P(A \cup B)-0.2 \leq 0.8]} $
$\Rightarrow P(B) \leq 0.8 $
$P(B) \text { cannot be } 0.9 .$
BETA
