GATE 2025 AR — Planning – Question 10

General Aptitude · Quantitative Aptitude: Probability, Statistics and Combinatorics · 2 marks · Multiple choice

A final year student appears for placement interview in two companies, S and T. Based on her interview performance, she estimates the probability of receiving job offers from companies S and T to be 0.8 and 0.6, respectively. Let $p$ be the probability that she receives job offers from both the companies. Select the most appropriate option.

$0 \leq p \leq 0.2$
$0.4 \leq p \leq 0.6$
$0.2 \leq p \leq 0.4$
$0.6 \leq p \leq 1.0$

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Correct answer: (B) $0.4 \leq p \leq 0.6$

Explanation

Let S and T denote receiving each offer. Their intersection cannot exceed either event, so p≤min(0.8, 0.6)=0.6.

Inclusion–exclusion gives P(S∪T)=0.8+0.6−p≤1, hence p≥0.4. Therefore **0.4≤p≤0.6, B**.

Both endpoints are attainable. At p=0.4, the S-only, T-only, both, neither probabilities are 0.4, 0.2, 0.4, 0. At p=0.6 they are 0.2, 0, 0.6, 0.2. No independence assumption is supplied; 0.8×0.6=0.48 is just one possible overlap, not a forced value.

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