Question

In a game, two players X and Y are tossing a coin alternately. Whoever gets a 'head' first, wins the game and the game is terminated. Find the chance that player X will win the game if he starts?

• A. 1/2
• B. 1/3
• C. 2/3
• D. 3/4

Answer 1

The correct option is C 2/3

$LetP=P\left(H\right)=\frac{1}{2},q=P\left(T\right)=\frac{1}{2},$

So A can win the game either in 1st or in 3rd or in 5th toss & so on ...

$\therefore P\left(A\right)=p+q^{2}p+q^{4}p+...$
$=p[1+q^2+q^4+...\infty ]$

$=\frac{p}{1-q^2}$
$=\frac{1/2}{1-{\left(1/2\right)}^2}=\frac{2}{3}$