Question

A jar contains infinitely many coins which come up Tails with proba- bility p. A person selects a coin from the jar and flips it on a table. In the following way, they continue flipping coins until all coins on the table show Tails: If the last flip came up Heads, they select a coin from the jar and flip it on the table. On the other hand, if the last flip came up Tails, they select a coin from the table which shows Heads and flip it on the table. Find the probability that this process eventually ends.

Answer 1

First of all the question is very ambiguously stated whoever has written it. Still I'm trying to answer a close question to this, which may help you I hope.

Given that,

probability of tail is p.

therefore, probability of head is (1-p)=q(say)

And here probably you have wanted to say that the event of flipping of coins will come to an end if head occurs.

If the first outcome is head, then required probability is q.

if the second outcome is head, required probability is pq

if the third outcome is head, then required probability is p²*q.

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.if the n-th outcome is head, then the required probability is p^(n-1) *q.And this is the general answer for n flips.