"A fair coin is flipped repeatedly. What is the probability that the 5th tail occurs before the tenth head?"(adsbygoogle = window.adsbygoogle || []).push({});

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

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

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

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# Fair Coin Qst

Can you offer guidance or do you also need help?

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