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A fair die is tossed repeatedly until a six obtained. Let X denote the number of tosses required. The conditional probability that `X ge 6` given `X g

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A fair die is tossed repeatedly until a six obtained. Let X denote the number of tosses required. The conditional probability that `X ge 6` given `X gt 3` equals A. `(125)/(216)` B. `(25)/(216)` C. `(5)/(36)` D. `(25)/(36)` Select the correct answer from above options

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Correct Answer - D `P({(Xge6)//(Xgt3)}=(P{Xgt3)//(Xge6)}*P(Xge6))/(P(Xgt3))` `=(1*[((5)/(6))^(5)*((1)/(6))+((5)/(6))^(6)*(1)/(6)+...oo])/([((5)/(6))^(3)*(1)/(6)+((5)/(6))^(4)*(1)/(6)+...oo])=(25)/(36)`

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