A fair coin is tossed repeatedly until it has landed Heads at least once and has...

A fair coin is tossed repeatedly until it has landed Heads at least once and has landed Tails at least once. Find the expected number of tosses.

Solutions

Expert Solution

Let be the probability of landing Heads.

The experiments will terminate in tosses,

1) When the toss is a Head preceded by Tails. Whose probability is

2) When the toss is a Tail preceded by Heads. Whose probability is

The above 2 events are disjoint.

The probability that the experiments will terminate in tosses is

Here . Hence,

The expected tosses is

Note that is the expected value of a Geometric distribution which is 2. Thus,

milcah answered 2 months ago

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