Question

Four persons A, B, C and D throw an unbiased die, turn by turn, in succession till one gets an even number and win the game. What is the probability that A wins if A begins ?
(A) \(\frac{1}{4}\)
(B) \(\frac{1}{2}\)
(C) \(\frac{7}{12}\)
(D) \(\frac{8}{15}\)

Answer 1

Ans: (D)
 Hint : \(P(A\) win \()=\left(\frac{1}{2}\right)+\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)+\left(\frac{1}{2}\right)^{8}\left(\frac{1}{2}\right)+\cdots\)
$$
=\frac{\frac{1}{2}}{1-\left(\frac{1}{2}\right)^{4}}=\frac{\frac{1}{2}}{\frac{15}{16}}=\frac{8}{15}
$$

Answer 2

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