how we know for getting two consecutive head expected number of trials is 6
Expectation example
Hey @rupeshjha909 we can derive it for the 2 the same way we did it for N.
Let the expected number of coin flips be x. The case analysis goes as follows:
a. If the first flip is a tails, then we have wasted one flip. The probability of this event is 1/2 and the total number of flips required is x+1
b. If the first flip is a heads and second flip is a tails, then we have wasted two flips. The probability of this event is 1/4 and the total number of flips required is x+2
c. If the first flip is a heads and second flip is also heads, then we are done. The probability of this event is 1/4 and the total number of flips required is 2.
Adding, the equation that we get is -
x = (1/2)(x+1) + (1/4)(x+2) + (1/4)2
Solving, we get x = 6.
Thus, the expected number of coin flips for getting two consecutive heads is 6.
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