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# 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) $$\frac{2}{9}$$

### 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) = $$\frac{3}{9}$$
= $$\frac{1}{3}$$

## Dicussion (1)

• 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) = $$\frac{3}{9}$$
= $$\frac{1}{3}$$