<PRE><B>Question 346172</B>
What is the probability that a number selected at random from the first 500 positive integers is (exactly) divisible by 6 or 9?



using as the first 500 positive integers 1 through 500 inclusively



there are 83 numbers divisible by 6 exactly between 1 and 500
(83 * 6 = 498)
there are 55 numbers divisible by 9 exactly between 1 and 500
(55 * 9 = 495)


probability of 6: 83/500 = 16.6/100 = 0.166 = 16.6 %


probability of 9: 55/500 = 11/100 = 11 %


probability of number being divisible by either 6 or 9: (83 + 55)/500
138/500 = 27.6/100 = 27.6 %


probability of number being divisible by either 6 or 9 but not both:


there are 27 numbers divisible by both 6 and 9 exactly between 1 and 500
(27 * 18 = 486)


138 - 27 = 111


probability of number being divisible by either 6 or 9 but not both: 
111/500 = 22.2/100 = 22.2 %
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