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An unbiased die is rolled untill two consecutive trials result in even numbered faces. The probability that exactly six trials are required to get con

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An unbiased die is rolled untill two consecutive trials result in even numbered faces. The probability that exactly six trials are required to get consecutive even numbered faces, is A. 5( 1 6 )6 B. 6( 1 2 )6 C. 4( 1 2 )6 D. ( 1 6 )6 Select the correct answer from above options

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Correct Answer - A Let Ei and Oi denote respectively the events of getting an odd numbered and even numbered face in ith trial. Then, Required probability =P{(O1∩O2∩O3∩O4∩E5∩E6)∪(O1∩E2∩O3∩O4∩E5∩E6)∪(O1∩O2∩E3∩O4∩E5∩E6)∪(E1∩O2∩O3∩O4∩E5∩E6)∪(E1∩O2∩E3∩O4∩E5∩E6} =5( 1 2 )6 [∵P(Oi=P(Ei)= 1 2 ,i=1,2,..,6]

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