Q) An unbiased die is rolled until a number greater than 4 appears on the die . Find the probability that an even number of tosses are needed.

A) Prob. that a number greater than 4 appears = 2/6 = 1/3

Prob. that a number less than or equal to 4 appears = 2/3

Prob. that an even no. of tosses are needed =

(2/3)*1/3 + (2/3)^3*1/3 + (2/3)^5 * 1/3 ......

= 2/9 (1 + (2/3)^2 + (2/3)^4 + (2/3)^6 + ....)

= 2/9 [ 1 / ( 5/9) ]

= (2/9)*(9/5)

= 2/5

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