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GATE 2025 ME – Question 5

General Aptitude · Quantitative Aptitude: Probability and Combinatorics · 1 mark · Multiple choice

P and Q play chess frequently against each other. Of these matches, P has won 80% of the matches, drawn 15% of the matches and lost 5% of the matches.

If they play 3 more matches, what is the probability of P winning exactly 2 of these 3 matches?

  1. $\frac{48}{125}$
  2. $\frac{16}{125}$
  3. $\frac{16}{25}$
  4. $\frac{25}{48}$

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Show answer and explanation

Correct answer: (A) $\frac{48}{125}$

Explanation

P wins each match with probability 0.8 and does not win with probability 0.2. The probability of exactly 2 wins in 3 matches is $\binom{3}{2}(0.8)^2(0.2) = 3 \times 0.64 \times 0.2 = 0.384 = \frac{48}{125}$.