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#1




Need help!
An unbiased coin is tossed repeatedly. What is the probability that the fourth occurrence of a head will take place before the second occurrence of a tail?
I don't understand why the answer is 3/16 instead of 5/32. Can someone help me out on this? Much appreciated!
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#2




Four heads on the first four flips, or three heads on the first four with a head on the fifth.

#3




Let be the number of heads flips before the second tails flip.
We want Hopefully the makes sense. There are several equivalent ways of defining a negative binomial and writing the PMF so if the PMF is unfamiliar the way I wrote it I’m using: Last edited by Z3ta; 12112017 at 01:39 AM.. 
#4




Using this formula, you would have to sum x from 4 to infinity.

#5




Quote:
My guess is that the writer of the problem intended for it to be solved your way, but this is the general solution if it weren’t so easy to just list out the possibilities. 
#10




Quote:
The probably of the first 4 being H is Now, you look at permuting HHHT for what takes place in the first 4 flips: However, there is only a 0.5 chance that the fifth flip is H, so the above is multiplied by 0.5 Since the above two are mutually exclusive, we get the total probability as being their sum:
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