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If a tail appears on the first flip of coin. If in the first flip, a tail occurs then it means that we have wasted one flip and we will have to do
more flips to reach our goal. The probability of this event is 1/2 and the total number of flips now required will be x+1. -
If a heads appears on the first flip of coin and a tails appears on the second flip. In this case it means that we have wasted two flips and we will have to do
more flips to reach our goal. Therefore the total number of flips now required will be x+2 and the probability of this event is 1/4. - The last case is, if we get two consecutive heads on two consecutive flips of the coin respectively. The probability of this event is 1/4 and the total number of flips required will be 2.
x = (1/2)(x+1) + (1/4)(x+2) + (1/4)2 x = 1/2 [ (1+x) + 1/2(2+x) + 1 ] x = 1/2 [ 1 + x + 1 + x/2 + 1 ] x / 4 = 3/2 x = 6Therefore, x = 6. Thus, the expected number of coin flips for getting two consecutive heads is 6.
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