WBJEE · Maths · Probability
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 & Solution
Correct Answer
(D) \(\frac{8}{15}\)
Step-by-step Solution
Detailed explanation
Hint: \(P(A\) win \()=\left(\frac{1}{2}\right)+\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)+\left(\frac{1}{2}\right)^{8}\left(\frac{1}{2}\right)+\cdots\) \(=\frac{\frac{1}{2}}{1-\left(\frac{1}{2}\right)^{4}}=\frac{\frac{1}{2}}{\frac{15}{16}}=\frac{8}{15}\)
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