To find the probability that the sum of a randomly selected number from \( P = \{1, 2, 3\} \) and \( Q = \{2, 3, 5\} \) is prime: Possible sums: 1 + 2 = 3 \(\text{prime})\) 1 + 3 = 4 \(\text{not prime})\) 1 + 5 = 6 \(\text{not prime})\) 2 + 2 = 4\(\text{not prime})\) 2 + 3 = 5 \(\text{prime})\) 2 + 5 = 7 \(\text{prime})\) 3 + 2 = 5 \(\text{prime})\) 3 + 3 = 6 \(\text{not prime})\) 3 + 5 = 8\(\text{not prime})\) Prime sums: \( 3, 5, 5, 7 \) (total: 4 favorable outcomes). Total outcomes: \( 3 \times 3 = 9 \). Probability: \(P = \frac{4}{9}\) Thus, the probability that the sum is prime is \(\frac{4}{9}\)