Problem 43575. Probabilities - More brains than luck
This problem is related to Problem 596. More luck than brains where the test suite checks 3 times if the outcome of the solution is a random number between 1 and 6.
Using brain, the "solver" would be interested in computing the probability of passing a general test (with some other interesting probabilities) where the suite checks C times if the outcome of the solution is a random number between 1 and N.
So, here is the problem:
- Each test in the suite checks if a random number between 1 and N is guessed.
- There are C tests in the suite.
Output these values, given inputs N,C,K:
- P = the probability of passing the test suite.
- XK = the probability that the number of times the function must be run to get a success (passing the test suite) is K.
- M = the mean number of times the function must be run to get a success.
You will see that, for N=6 and C=3, then M=216.
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