# Fair Coin Qst

1. Oct 24, 2007

### leakin99

"A fair coin is flipped repeatedly. What is the probability that the 5th tail occurs before the tenth head?"

What I have so far:

So the 5th tail has to come before 10th head. So if we take getting a tails as success and after the 9th head, we MUST have 5 tails --> we can only have 14 flips or less(but more than 4, since we're looking for 5 Tails).

let X be the # of flips required to get a 5th tail and since X is a negative binomial rv(conditions above, hopefully)

The lower bound on the sum is 5, and the upperbound on the sum is 14. (n-1)C4 is n-1 "CHOOSE" 4

$$\sum$$P(X=n) = $$\sum$$[(n-1)C(4)](0.5)$$^{5}$$(0.5)$$^{n-5}$$

I don't know if I am doing this right because I am not 100% sure if X is a negative binomial RV. Can anyone maybe explain the setting up process or something.

Thanks