Set S consists of all prime integers less than 10. If two different numbers are chosen from set S at random, what is the probability that the product of these numbers will be greater than the product of the numbers that were not chosen?
A. 1/3
B. 2/3C. 1/2D. 7/10E. 4/5

Question

Set S consists of all prime integers less than 10. If two different numbers are chosen from set S at random, what is the probability that the product of these numbers will be greater than the product of the numbers that were not chosen?
A. 1/3
B. 2/3C. 1/2D. 7/10E. 4/5

Rakesh Rakesh · Answer

Set S = {2, 3, 5, 7} (all primes less than 10).We choose 2 numbers out of 4. Total combinations = 6.Now compare the product of the chosen 2 numbers vs the product of the 2 not chosen.(2,3) → 6 vs 35 → No(2,5) → 10 vs 21 → No(2,7) → 14 vs 15 → No(3,5) → 15 vs 14 → Yes(3,7) → 21 vs 10 → Yes(5,7) → 35 vs 6 → YesOut of 6 cases, 3 are successful ⇒ Probability = 3/6 = 1/2Answer: C. 1/2

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