An unbiased die is rolled until a number greater than 4 appears. The probability that an even number of trials are needed, is

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MARKS Content Team · Accepted Answer

Correct answer: (B) 2/5. p = Probability of success s = 2/6 = 1/3 q = Probability of failure f = 1 - 1/3 = 2/3 The probability that success occurs in even number of trials =p(fs)+p(fffs)+p(fffffs)+..... =qp+q^3p+q^5p+…=qp/(1-q^2) = 2/3 × 1/3 1 - 2 3^2 = 2/9 1 - 4/9 = 2/9 × 9/5 = 2/5

An unbiased die is rolled until a number greater than $4$ appears. The probability that an even number of trials are needed, is

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