Question

$A$ and $B$ toss a coin alternatively till one of them gets a head and wins the game. If $A$ begins the game, the probability $B$ wins the game is

• A. $1/2$
• B. $1/3$
• C. $1/4$
• D. $2/3$

Answer 1

Answer: (B)

$1/3$

$P(B$ wins$)$ $=\frac{1}{2}\left(\frac{1}{2}\right)+{\left(\frac{1}{2}\right)}^3+\left(\frac{1}{2}\right)+{\left(\frac{1}{2}\right)}^5\left(\frac{1}{2}\right)+.....=\frac{1}{3}$