Originally posted by: Chiropteran
Originally posted by: TuxDave
Someone can just write a program.
Step #1: Pick a coin (19/20 fair), (1/20 biased)
Step #2: Flip 4 times. If not all heads, start over to step #1. If all four heads, add one to "Total Samples"
Step #3: Flip a coin, if heads, add one to "Total samples that had head on 5th flip"
Step 3/Step 2. You'll see the answer is closer to KoolAidKid's answer. I guarantee it.
But your step 2 wasn't mentioned by the OP.
He didn't say "flip coins 4 times until you successfully flip one heads all 4 times"
There are 20 coins.
One is picked at random.
It is flipped 4 times, and all 4 flips are heads.
The chance of that coin being the broken coin is 5%, 1/20. It can't possibly be higher because it was picked at random BEFORE it was known that the 4 flips were all heads.
So 5% of the time it'll be heads, the other 95% of the time there is a 50/50 chance of it being heads. 52.5% chance that it will be heads on the 5th flip.