A die is tossed until the sum of the rolls is 15 or greater.
What is the most likely total? What is the the least likely total which can occur?
As the solution points out, there is only 1 way to get a total of 20, 2 ways to get a 19, 3 ways to get an 18, 4 ways to get a 17, 5 ways to get a 16 and 6 ways to get a 15
Altogether 21 ways. They are not equally likely (because the target is only 15) but it is probably close to equal.
This makes the probability of getting 20 roughly equal to 1/21 = .0476
This makes the probability of getting 15 roughly equal to 6/21 = .2857
These are very close to the actual probabilities, which according to Charlie are .047257 and .286114 respectively.
If the target n was very large (say 100 or 1,000 or 10,000), then I would expect the actual probabilities of achieving n+5 and n to be virtually indistinguishable from 1/21 and 6/21, respectively.
Edited on May 25, 2017, 10:04 pm
Quick but not so dirty probabilities
