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No, on two counts.

The sample space is the possible outcomes of the experiment, not the NUMBER of possible outcomes. And, as far as this experiment is concerned, there is no way to distinguish between the two occurrences of b and i. So there are, in fact, only 9 possible outcomes. Two of these outcomes have a higher probability but that is a different matter.

The sample space is {p, r , o , b, a, i, l, t, y} a set of cardinality 9.

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Q: What is the sample space for choosing a letter from the word probability?
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What is the sample space for choosing the letter from the word probability?

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