What is the probability of getting a number divisible by 3 when a random number is chosen from 1 to 50?

Instruction: Choose one integer uniformly from 1 through 50 inclusive. Calculate the probability it is divisible by 3, and explain how the result changes for 0 through 50 inclusive.

Context: This question checks the candidate's ability to apply divisibility rules and basic probability principles.

Updated

Official answer

The multiples of 3 are 3,6,9,...,48: there are floor(50/3) = 16. Under uniform sampling of the 50 integers, the probability is 16/50 = 8/25 = 0.32, or 32%.

The endpoint matters:0 is not included. If the range were 0 through 50 inclusive, there would be 51 possible integers and 17 multiples including 0, giving 17/51 = 1/3.

Follow-up: For a positive integer N, uniform sampling from 1 through N gives floor(N/3)/N. If sampling is nonuniform, count ratios are insufficient; sum the probabilities of the multiples instead.

Assessment: Look for an explicit integer range, inclusive endpoints and a justified uniform sample space.

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