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

A.

\(\frac{5}{9}\)

B.

1\(\frac{4}{9}\)

C.

\(\frac{1}{3}\)

D.

\(\frac{2}{9}\)

Correct answer is C

p = { 1, 2, 3}

Q = {2, 3, 5}

prob(prime number) = prob(1 and 2) or

= prob(2 and 3) or

= prob(3 and 2)

There are three possibilities of the sum being prime

Total possibility = 9

probability(sum being prime) = \(\frac{3}{9}\)

= \(\frac{1}{3}\)