What is the probability that a number selected at random from the set {2, 3, 7, 12, 15, 22, 72, 108} will be divisible by both 2 and 3?
A. \(\frac{1}{4}\)
B. \(\frac{3}{8}\)
C. \(\frac{3}{5}\)
D. \(\frac{5}{8}\)
E. \(\frac{7}{8}\)
Answer (3)
∣Ω∣ = 8 ∣ A ∣ = 3 P ( A ) = ∣Ω∣ ∣ A ∣ P ( A ) = 8 3
Total amount of numbers in the set = 8 .
Total amount that are divisible by both 2 and 3 = 3 .
So the probability of picking one of them is 3/8 = 37.5 percent .
The probability that a number selected from the set {2, 3, 7, 12, 15, 22, 72, 108} is divisible by both 2 and 3 is 8 3 . This is based on the total numbers in the set and counting those which are divisible by 6. Therefore, the correct option is B. 8 3 .
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