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GATE 2025 ME – Question 10

General Aptitude · Quantitative Aptitude: Probability 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.

  1. $0 \leq p \leq 0.2$
  2. $0.4 \leq p \leq 0.6$
  3. $0.2 \leq p \leq 0.4$
  4. $0.6 \leq p \leq 1.0$

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

Explanation

For any two events, $P(S \cap T) \leq \min(0.8, 0.6) = 0.6$. Also $P(S \cap T) \geq P(S) + P(T) - 1 = 0.4$. So $0.4 \leq p \leq 0.6$.