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

Question

An unbiased die is rolled until a number greater than 4 appears. The probability that an even number of trials are needed, is, 1 2, 2 5, 1 5, 2 3

MARKS App · Accepted Answer

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 ( f s ) + p ( f f f s ) + p ( f f f f f s ) + . . . . . = qp + q 3 p + q 5 p + … = qp 1 - q 2 = 2 3 × 1 3 1 - 2 3 2 = 2 9 1 - 4 9 = 2 9 × 9 5 = 2 5

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