Question
An integer is chosen at random from the first 200 positive integers. The probability that the integer chosen is divisible by 6 or 8 is:

1/3

1/4

1/5

None of these
diffcult
Solution
1/4
Let E = divisible by 6
F = divisible by 8
Number divisible by 6 are: 6, 12, 18, 24,….198 i.e.. There are 33 numbers in first 200 positive integers that are divisible by 6.
Number divisible by 8 are: 8, 16, 24, 32,….200 i.e.. There are 25 numbers in first 200 positive integers that are divisible by 8.
Number divisible by 6 and 8 both are: 24,….192. These are 8 numbers in first 200 positive integers that are divisible by both 6 and 8.
P(integer is divisible by 6 and 8) = P(E ∪ F) = P (E) + P(F)
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