ACT Math · Probability and counting

A spinner has 8 equal sections numbered 1 through 8. What is the probability that a spin lands on a multiple of 3?

A spinner has 8 equal sections numbered 1 through 8. What is the probability that a spin lands on a multiple of 3?

Answer and explanation

Answer: B: 1/4

The multiples of 33 from 11 to 88 are 33 and 66, so there are 22 favorable sections out of 88 equally likely sections. The probability is 28=14\frac{2}{8}=\frac{1}{4}, choice B. Choice A (18\frac{1}{8}) counts only one favorable section. Choice C (38\frac{3}{8}) counts three, perhaps by including 99 or by counting 00, neither of which is on the spinner. Choice D (12\frac{1}{2}) is the probability of an even number or of an odd number, not of a multiple of 33. List the favorable outcomes explicitly to avoid miscounting.

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