Question

Two persons A and B are playing a game of rolling 2 dice alternately. The person who first gets the sum of the numbers appearing on the dice as a prime number will win the game. If A starts the game, then the probability of B winning the game is

• A. \(\dfrac{12}{19}\)
• B. \(\dfrac{5}{19}\)
• C. \(\dfrac{7}{19}\)
• D. \(\dfrac{14}{19}\)

Hint:

When players take alternate independent turns, the probability usually forms an infinite geometric series. Identify the common ratio and apply \[ \boxed{1+r+r^2+\cdots=\frac1{1-r}}. \]

Answer 1

The Correct Option is C