Probability Test

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Probability Test - 6

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Question 1
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Assertion & Reasoning
This section contains 4 reasoning type questions. Each questions has 4 choices (a), (b), (c) and (d), out of which ONLY ONE is correct.

Let A and B be two event such that P(AB) ≥ 3/4 and 1/8 ≤ P(AB) ≤ 3/8
Statement–1: P(1) + P(2) ≥ 7/8
Statement–2: P(1) + P(2) ≤ 11/8

A
Statement–1 is True, Statement–2 is True; Statement–2 is a correct explanation for Statement–1

B
Statement–1 is True, Statement–2 is True; Statement–2 is NOT a correct explanation for Statement–1

C
Statement–1 is True, Statement–2 is False

D
Statement–1 is False, Statement–2 is True

Solution

P(AB) = P(1) + P(2) – P(AB)
∴ 1 ≥ P(1) + P(2) – P(AB) ≥ 3/4
P(1) + P(2) – 1/8 ≥ 1/8 ≥ 3/4 (since min. value of P(AB) = 1/8)
P(1) + P(2) ≤ 1/8 + 3/4 = 7/8
As the max. value of P(AB) = 3/8, we get
1 ≥ P(1) + P(2) – 3/8
P(1) = P(2) ≤ 1 + 3/8 = 11/8.
Hence, option D is correct.