A pair of dice is thrown. What is the probability of getting the sum of numbers on the two faces an odd-prime number?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{7}{18}\)
Two dice give \(6\times6=36\) equally likely outcomes. The sum lies between 2 and 12, and the odd primes in that range are 3, 5, 7 and 11 (2 is prime but even).
Sum 3: (1, 2), (2, 1) — 2 outcomes
Sum 5: (1, 4), (2, 3), (3, 2), (4, 1) — 4 outcomes
Sum 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) — 6 outcomes
Sum 11: (5, 6), (6, 5) — 2 outcomes
Favourable outcomes \(=2+4+6+2=14\), so the probability \(\displaystyle =\frac{14}{36}=\frac{7}{18}\)