Question

A and B are playing a game of chess. A can win or lose a round with probabilities $\frac{1}{2}$ and $\frac{1}{3}$ respectively. $\frac{1}{6}$ is the probability to draw a round. The person who wins two round is the winner.
What is the probability that B wins first round and Adoes not wins any round in first five round and A wins the game in exactly ten rounds?

• A. $2\left(\frac{1}{6}\right)^9$
• B. $2\left(\frac{1}{6}\right)^8$
• C. $7\left(\frac{1}{6}\right)^9$
• D. $7\left(\frac{1}{6}\right)^8$

Answer 1

Answer: (B)

Probability $=\frac{1}{3}\left(\frac{1}{6}\right)^7 \cdot{ }^4 C _1\left(\frac{1}{2}\right) \times \frac{1}{2}=\frac{2}{6^8}$