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
\(\frac{11}{12}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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)
= \(\frac{4}{12} + \frac{3}{12} = \frac{7}{12} - \frac{1}{2}\) = \(\frac{4 + 3 - 1}{12}\)
= \(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #36633)