SOLUTION: What is the probability that number selected at random from the first 1,000 postitive integers is (exactly) divisible by 77 or 49?

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Question 1071019: What is the probability that number selected at random from the first 1,000 postitive integers is (exactly) divisible by 77 or 49?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Let A be the event that a positive integer 1000 or less 
is exactly divisible by 77.

Let B be the event that a positive integer 1000 or less 
is exactly divisible by 49.

We want:



To find N(A) we divide 1000/77 = 12.98701299, and round 
down to 12.

So P%28A%29=N%28A%29%2F1000=12%2F1000+=+0.012

To find N(B) we divide 1000/49 = 20.40816327, and round 
down to 20.

So P%28B%29=N%28B%29%2F1000=20%2F1000+=+0.020

For an integer to be divisible by both 77 and 49 it has
to be divisible by 77*49 or 539, and only one positive
integer in the first 1000 positive integer that is divisible
by 539 is 539 itself.  So N(A and B) = 1

So 



becomes:



Answer: 0.031

Edwin