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When 2 numbers are selected from the integers from 1 to 21 i

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by Max@Math Revolution » Mon Jul 30, 2018 11:34 pm

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[Math Revolution GMAT math practice question]

When 2 numbers are selected from the integers from 1 to 21 inclusive, what is the probability that the 2 selected numbers are prime numbers?

A. 2/15
B. 1/5
C. 1/3
D. 4/15
E. 2/5
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by Max@Math Revolution » Wed Aug 01, 2018 11:27 pm
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There are 8 prime numbers between 1 and 21, inclusive: 2, 3, 5, 7, 11, 13, 17 and 19.
So, there are 8C2 ways of selecting 2 numbers from these 8 prime numbers.
There are 21C2 ways of selecting 2 numbers from the 21 numbers from 1 to 21, inclusive.
Thus, the probability that the 2 selected numbers are prime numbers is 8C2 / 21C2 = ( 8*7 / 1*2) / ( 21*20 / 1*2 ) = 8*7 / 21*20 = 2/15.

Therefore, the answer is A.

Answer: A
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by Scott@TargetTestPrep » Fri Aug 10, 2018 5:52 pm
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

When 2 numbers are selected from the integers from 1 to 21 inclusive, what is the probability that the 2 selected numbers are prime numbers?

A. 2/15
B. 1/5
C. 1/3
D. 4/15
E. 2/5
The prime numbers between 1 and 21 are 2, 3, 5, 7, 11, 13, 17, and 19. So there are 8 primes between 1 and 21, and the number of ways to select 2 of them is 8C2 = (8 x 7)/2 = 28.
The number of ways to select 2 of 21 numbers is 21C2 = (21 x 20)/2 = 210.

Therefore, the probability is 28/210 = 4/30 = 2/15.

Alternate Solution:

The primes numbers between 1 and 21 are 2, 3, 5, 7, 11, 13, 17, and 19. So there are 8 primes between 1 and 21. The probability that the first number chosen is prime is 8/21, and the probability that the second number chosen is prime is 7/20. Thus, the probability of choosing 2 primes out of two selections is 8/21 x 7/20 = 56/420 = 2/15.

Answer: A

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