Waiting for double six
Topic: Random variables and distributions · more questions on this topic
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Two fair dice are thrown repeatedly until their sum is 12.
Find the probability that this takes exactly 10 throws.
Find the probability that it takes at most 100 throws.
Worked answer (click to show)
A throw shows double six with probability 1/36. The number of throws required is geometric, starting at 1.
(35/36)^9(1/36)\approx 0.0216.
The probability that the first 100 throws all fail is (35/36)^{100}, so the probability of success by throw 100 is 1-(35/36)^{100}\approx 0.940.