GATE 2025 AR — Architecture – Question 5

General Aptitude · Quantitative Aptitude: Probability, Statistics 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?

$\frac{48}{125}$
$\frac{16}{125}$
$\frac{16}{25}$
$\frac{25}{48}$

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Show answer and explanation

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

Explanation

Use the intended model of independent future matches with a constant win probability 0.8, estimated from the past results. A non-win includes both a draw and a loss, so its probability is 0.15+0.05=0.20.

Choose which two of three matches are wins:
$$P=\binom32(0.8)^2(0.2)=0.384=\frac{48}{125}.$$
Thus **A**. Using 0.05 for the third match would count only two wins and a loss, omitting two wins and a draw. Past percentages alone do not establish independence; it is the probability model intended by the question.

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