Question

A & B having equal skill are playing a game of best of 5 points. After A has won two points & B has won one point, the probability that A will win the game is

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{3}{4}$
• D. none

Answer 1

Answer: (C)

$\frac{3}{4}$

Total possible cases are A wins the next point and wins the game, B wins the next two point and wins the game, B wins the next point followed by A winning the next point. As for the 4th point, as both players have equal skill, therefore probability for the next point is $\frac{1}{2}$. When A wins the next point $P=\frac{1}{2}$, when B wins the next point followed by A winning the next point is $P=\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}$. Net probability by which A wins the game is hence $\frac{3}{4}$.