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I'm kind of embarrassed that I don't fully get this, but I assume it is because the example is using letters for a sample space instead of numbers.

Sample space = {a,b,c,d,e,f} with equal probability  outcome |  a  |  b  |  c  |  d  |  e  |  f  | x       |  0  |  0  | 1.5 | 1.5 |  2  |  3  | 

Is this saying that P(X=0) = a + b? Or P(X=0) = 1/6 + 1/6?

Could someone please explain this is simple terms (like a dice throw example, perhaps)?

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    @MaxMackie Done! with minor changes.2012-10-10

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There are six equally likely outcomes a, b, c, d, e, f. Think of them as the outcomes of a roll of a fair die whose faces are marked a, b, c, d, e, f instead of the usual $1, 2, 3, 4, 5, 6$. Suppose you win an amount $X$ whose value depends on the outcome of the die roll. The table shows that you win $0$ if you roll an a or a b, $1.5$ if you roll a c or a d, $2$ if you roll an e, and $3$ you roll an f. So X takes on values $0, 1.5, 2$, and $3$ with probabilities $\frac{1}{6}+\frac{1}{6} = \frac{1}{3}$, $\frac{1}{6}+\frac{1}{6} = \frac{1}{3}$, $\frac{1}{6}$ and $\frac{1}{6}$ respectively,