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I am working on this problem, have searched my textbook, this forum, etc and am still as lost. I suspect I need to (in some form) use the formula P(AB)/P(B) = P(A) as it is the integral formula of this section. Any suggestions or hints are greatly appreciated.

A fair coin is tossed until a head is obtained for the first time. If this experiment is performed 3 times, what is the probability that exactly the same number of tosses will be required for each of the 3 performances?

Note: the answer is 1/7

My work thus far:

I know n-1 tails must be obtained in each performance

Events:

Ai = a head is obtained on the ith trial

Bi = " " tail " "

P(Ai) = 0.5

P(Bi) = 0.5