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If 2 prime numbers are chosen less than 100 without repetition, then what is the probability that their sum will be an odd number?
\(A. \frac{6}{75}\)
\(B. \frac{3}{75}\)
\(C. \frac{1}{12}\)
\(D. \frac{276}{300}\)
\(E. \frac{273}{300}\)
\(A. \frac{6}{75}\)
\(B. \frac{3}{75}\)
\(C. \frac{1}{12}\)
\(D. \frac{276}{300}\)
\(E. \frac{273}{300}\)
08 Jul 2019, 00:12
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Kinshook
If 2 prime numbers are chosen less than 100 without repetition, then what is the probability that their sum will be an odd number?
\(A. \frac{6}{75}\)
\(B. \frac{3}{75}\)
\(C. \frac{1}{12}\)
\(D. \frac{276}{300}\)
\(E. \frac{273}{300}\)
\(A. \frac{6}{75}\)
\(B. \frac{3}{75}\)
\(C. \frac{1}{12}\)
\(D. \frac{276}{300}\)
\(E. \frac{273}{300}\)
for sum to be odd : one number must be even
nly even prime is 2 nd total prime number less than 100 are 25
so 1c1(that is always choose 2) * 24c1(choose anyone of 24) / 25c2
so answer will be 2/25 which multiply by 3 in num nd den will be 6/75
13 Feb 2022, 12:57
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Kinshook
If 2 prime numbers are chosen less than 100 without repetition, then what is the probability that their sum will be an odd number?
\(A. \frac{6}{75}\)
\(B. \frac{3}{75}\)
\(C. \frac{1}{12}\)
\(D. \frac{276}{300}\)
\(E. \frac{273}{300}\)
\(A. \frac{6}{75}\)
\(B. \frac{3}{75}\)
\(C. \frac{1}{12}\)
\(D. \frac{276}{300}\)
\(E. \frac{273}{300}\)
The prime numbers less than 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
There are 25 primes in total, and only 1 is even.
For this question, I would probably use counting techniques, but we can also saw that using probability rules quite quickly.
The key here is to recognize that, in order for the sum to be odd, one number must be ODD, and the other must be EVEN. So,....
P(sum is odd) = P(1st number is odd AND 2nd number is even OR 1st number is even AND 2nd number is odd)
= [P(1st number is odd) x P(2nd number is even)] + [P(1st number is even) x P(2nd number is odd)]
= [24/25 x 1/24] + [1/25 x 24/24]
= 1/25 + 1/25
= 2/25
Check answer choices.... not there!
However, 6/75 is equivalent to 2/25, which means the correct answer is A
