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A and B toss ...

Question

A and B toss a coin alternatively, the first to show a head being the winner. If A starts the game, the chance of his winning is?

A

5 / 8

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B

1 / 2

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C

1 / 3

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D

2 / 3

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Solution

The correct option is D $2 / 3$
For A to win outcomes can be H,TTH,TTTTH,...
= ${1 / 2}^{1} + {1 / 2}^{3} + {1 / 2}^{5} + . . .$
= $= \frac{1 / 2}{1 - 1 / 4} = 2 / 3$

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