You have a magic coin, where the probability of the coin facing heads up changes per day. The probability of the coin landing heads up can be expressed by (499+x)/10000, where x is the day number up to 9500.

What is the probability that the coin will face heads up exactly once by the 200th day if you take one trial per day?

Question

You have a magic coin, where the probability of the coin facing heads up changes per day.  The probability of the coin landing heads up can be expressed by (499+x)/10000, where x is the day number up to 9500.

What is the probability that the coin will face heads up exactly once by the 200th day if you take one trial per day?

turingtest · Answer

what exactly does "face up by the 200th day" mean? does it mean that it only faces up heads once, or at least once?

turingtest · Answer

exactly once or at least once?

anonymous · Answer

*the probability that the coin faces heads up at least once by the 200th trial.

turingtest · Answer

oh good, the other one would have been tricky
find the probability that heads did not come up in 200 trials and call that event A
the probability that heads did come up is then the compliment, 1-P(A)

anonymous · Answer

I was wrong, exactly once.

turingtest · Answer

ok then it's a bit trickier....
we have 200 disjoint events (heads on day 1, tails the next 199 days; heads on day 2, etc)
so let's see if we can come up with a version of the total probability law that can help us here
what would be the probability that we got heads on day K ?

anonymous · Answer

come back in some time, I have dinner