Two dice are tossed. What is the probability that the sum of the numbers on the two dice is a prime number?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\frac{5}{12}\)
Two dice give \(6\times6=36\) equally likely outcomes. The sum lies between 2 and 12, and the primes in that range are 2, 3, 5, 7 and 11. The outcomes giving each prime sum:
Sum 2: (1, 1) — 1 outcome
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 \(=1+2+4+6+2=15\), so the probability \(\displaystyle =\frac{15}{36}=\frac{5}{12}\).
Tip: For two dice, the number of ways to get the sums 2, 3, ..., 7 is 1, 2, 3, 4, 5, 6, and it falls back 5, 4, 3, 2, 1 for the sums 8 to 12. Knowing this saves listing the pairs.