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

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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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) = \(\frac{3}{9}\)
    = \(\frac{1}{3}\)