If a number is chosen at random from the set {x: 4 \(\leq x \leq...

WAEC 2011

If a number is chosen at random from the set {x: 4 \(\leq x \leq 15\)}. Find the probability that it is a multiple of 3 or a multiple of 4

A. \(\frac{1}{2}\)
B. \(\frac{5}{12}\)
C. \(\frac{7}{12}\)
D. \(\frac{11}{12}\)

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Correct Answer: Option A

Explanation

set = 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

multiples of 3 = 6, 9, 12, 15

multiples of 4 = 4, 8, 12

Prob(multiples of 3 or 4) = Prob(multiple of 3) + pro(multiple of 4) - pro(3 ∩ 4)

= \(\frac{4}{12} + \frac{3}{12} = \frac{7}{12} - \frac{1}{2}\) = \(\frac{4 + 3 - 1}{12}\)

= \(\frac{1}{2}\)

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