Arnav rolls two dice simultaneously. What is the probability of Arnav getting two numbers whose sum is a prime number?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{5}{12}\)
Two dice give \(6\times6=36\) equally likely ordered pairs. The sums run from 2 to 12, and the primes among them are 2, 3, 5, 7 and 11.
Sum 2: (1, 1), 1 way
Sum 3: (1, 2), (2, 1), 2 ways
Sum 5: (1, 4), (2, 3), (3, 2), (4, 1), 4 ways
Sum 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1), 6 ways
Sum 11: (5, 6), (6, 5), 2 ways
Favourable outcomes \(=1+2+4+6+2=15\), so probability \(\displaystyle =\frac{15}{36}=\frac{5}{12}\)