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GATE 2015 CS – Question 9

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

The probabilities that a student passes in Mathematics, Physics and Chemistry are $m$, $p$, and $c$ respectively. Of these subjects, the student has 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Following relations are drawn in $m$, $p$, $c$:

(I) $p + m + c = 27/20$

(II) $p + m + c = 13/20$

(III) $(p) \times (m) \times (c) = 1/10$

  1. Only relation I is true.
  2. Only relation II is true.
  3. Relations II and III are true.
  4. Relations I and III are true.

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Show answer and explanation

Correct answer: (D) Relations I and III are true.

Explanation

Passing exactly three has probability $0.50 - 0.40 = 0.10$, and passing exactly one has probability $0.75 - 0.50 = 0.25$. Since $m + p + c$ is the expected number of passes, $m + p + c = 1(0.25) + 2(0.40) + 3(0.10) = 1.35 = \frac{27}{20}$, so I is true. The product $mpc$ is the probability of passing all three, which is $0.10 = \frac{1}{10}$, so III is true.