If a number is selected at random from each of the sets p = {1, 2, 3} and Q = {2, 3, 5}, find the probability that the sum of the numbers is prime
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 \(\frac{4}{9}\)
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