Question 559487
We can easily find the probability of all three matching symbols. If we fix the first symbol, then the other two must both be the same, so the probability is 1/15^2, or 1/225. Equivalently, the odds are 1:224.


Finding the probability of exactly two of the same is a little trickier. Several ways to do this, but we can subtract the probability of none of them being the same and the probability of all three the same from 1. Equivalently,


*[tex \LARGE P(2 same) = 1 - P(none) - P(3 same)]


We know that P(3 same) = 1/225. P(none same) = 15*14*13/(15^3) = 182/225. Therefore,


*[tex \LARGE P(2 same) = 1 - \frac{182}{225} - \frac{1}{225} = \frac{42}{225} = \frac{14}{75}]


Therefore the odds are 14:61.


Note that slot machines, realistically, are non-random, and the probabilities are often much lower.