<span>There are 24 who like both rock and country. There are 8 who like all 3 types, and these eight have been counted under the 24. This means that the number who like rock and country but not jazz is 24 - 8 = 16.
We are given a total of 155 who like country. We subtract the 16 who like both rock and country, and are left with 139 people who like country but not rock. (It does not matter whether they like jazz or not).
The probability is 155 out of the total of 500, so 155/500 = 31/100 = 0.31.
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