Find the probability that a number chosen at random from the integers between 5 and 16 inclusive is a multiple of 3 or a mutiple of 2

5 / 6

Explanation:

Given that :

Sample space = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}

Multiples of sample space

3 = (6, 9, 12, 15)

2 = (6, 8, 10, 12, 14, 16)

Probability, p = required outcome / Total possible outcomes

Probability of picking a number which is a multiple of 2 or 3

P(multiple of 2) = 6 / 12 = 1/2

P(multiple of 3) = 4 / 12 = 1 /3

P(multiple of 2) or P(multiple of 3)

P(multiple of 2) + P(multiple of 3)

1/2 + 1/3

= (3 + 2) / 6

= 5/6