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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. 48/125
2. 16/125
3. 16/25
4. 25/48

Correct answer: 16/25

Solution

For exactly 2 wins in 3 independent matches, the binomial probability is \(\binom{3}{2}(0.8)^2(0.2)\). This equals \(3 \times 0.64 \times 0.2 = 0.384 = 48/125\). The provided answer key text does not match the probability calculation, but the mathematically correct result from the options is 48/125.

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