Question 559487: A slot machine has three reels, each reel has 15 symbols. What are the odds of two of the same symbols hitting on a spin? and What are the odds of all three symbols matching on a spin?
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! 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,
 = 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,
 = 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.
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