P and Q play chess frequently against each other. Of these matches, P has won…
2025
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?
Answer: A. \(\frac{48}{125}\) — Let a win have probability \(p=\frac{80}{100}=\frac45\). In \(3\) matches, the number of wins is binomial with \(n=3\). For exactly \(2\) wins, choose which…
- A.
\(\frac{48}{125}\)
- B.
\(\frac{16}{125}\)
- C.
\(\frac{16}{25}\)
- D.
\(\frac{25}{48}\)
Show answer & explanation
Correct answer: A
Let a win have probability \(p=\frac{80}{100}=\frac45\). In \(3\) matches, the number of wins is binomial with \(n=3\). For exactly \(2\) wins, choose which \(2\) matches are wins in \(\binom{3}{2}\) ways, then multiply by \((\frac45)^2\) for the wins and \(\frac15\) for the remaining non-win: \(\binom{3}{2}(\frac45)^2(\frac15)=3\cdot\frac{16}{25}\cdot\frac15=\frac{48}{125}\). Thus the required probability is \(\frac{48}{125}\).