**If a number is selected at random from each of the sets p = {1, 2, 3} and Q = {2...**

### Question

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

### Options

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

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

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

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

The correct answer is C.

### Explanation:

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) = \(\frac{3}{9}\)

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

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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) = \(\frac{3}{9}\)

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