IIT JEE 1982 Maths - 'Adapted' - Subjective to Multi-Correct Q15
A and B are two candidates seeking admission in IIT. The probability that A is selected is 0.5 and the probability that A and B are selected is at most 0.3. Then the probability of B getting selected can be
- (A) 0.2
- (B) 0.3
- (C) 0.5
- (D) 0.9
Enter your answer as a 4-digit string of 1s and 9s – 1 for correct option, 9 for wrong. For example: if and are correct, and and are incorrect, enter 1199. None, one or all may also be correct.
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The answer is 1119.
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1 solution
This can be done using simple Venn Diagram analogy.
Given P ( A ) = 0 . 5 and P ( A ⋂ B ) ≤ 0 . 3 . Let P ( B ) = ρ .
P ( A ) + ρ + P ( A ⋂ B ) + P ( A ˉ ⋂ B ˉ ) = 1 ⟹ ρ + P ( A ˉ ⋂ B ˉ ) ≤ 0 . 8 .
Thus A,B,C are possible but D isn't, leading to the answer of 1 1 1 9 .