Dan is a good, but not great, chess player. Based on past tournament experience, his chances of winning any single game are . What is the probability that Dan will win the second and third games of a five-game match and lose all the others?

My choices are (16/3,125) or (64/3,125) or (72/3,125) or (0) or (1)

Question

Dan is a good, but not great, chess player. Based on past tournament experience, his chances of winning any single game are . What is the probability that Dan will win the second and third games of a five-game match and lose all the others?

My choices are (16/3,125) or (64/3,125) or (72/3,125) or (0) or (1)

kropot72 · Answer

There is a missing value after the words "...his chances of winning any single game are ."

anonymous · Answer

sorry, 4/5

kropot72 · Answer

Dan's probability of losing any single game is 1 - (4/5) = 1/5
The probability of Dan losing 3 out of 5 games is given by
$$P(3\ losses)=\left(\begin{matrix}5 \ 3\end{matrix}\right)0.2^{3}\times 0.8^{2}= ?$$