Two numbers are said to be relatively prime if they share no common positive factors other than 1. Set S contains the set of integers from 1 to 1,000, inclusive. What is the probability that a number chosen from S is relatively prime to 1,000?
Correct answer: D
Explanation
We need all numbers between 1 and 1000 that are co-prime.
Between 1 to 10 there are 4 : 1,3,7,9
Take the period of 10's , we have 100 periods of 10's between 1 to 1000
So the total number of co-primes = 400
Now, the simple part ...
Probability = 400/1000 (i.e picking a co-prime from the first 1000 numbers )
Ans: 2/5 D
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