Independent Events Question: Coin Tossing

[chapone]

Hello all,

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

 

[Rogerio]

Well, the length of the first sequence may be 1 , 2 , 3 , etc...

Suppose the length of the first sequence is 1 (you got a head at the first toss).
Then, what is the probability of obtaining again the same sequence 2 more times?

And if the length of the first sequence was 2 , what would be the probability of repeating the results 2 more times?

And if the length was 3?

And then, finally, you should sum all this parcels...

 

[chapone]

Well, the length of the first sequence may be 1 , 2 , 3 , etc...

Suppose the length of the first sequence is 1 (you got a head at the first toss).
Then, what is the probability of obtaining again the same sequence 2 more times?

And if the length of the first sequence was 2 , what would be the probability of repeating the results 2 more times?

And if the length was 3?

And then, finally, you should sum all this parcels...

Thank you, that was very helpful!