If a four-sided die is rolled twice, what is the probability of getting a sum of 5?

Instruction: List all 16 ordered outcomes of two independent rolls of a fair die numbered 1–4. Identify those summing to five and calculate the probability.

Context: This question assesses the candidate's ability to enumerate possible outcomes and calculate their probability in a simple dice game scenario.

Updated

Official answer

Assume two independent rolls of a fair die numbered 1–4. The 16 equally likely ordered outcomes are:

(1,1) (1,2) (1,3) (1,4)
(2,1) (2,2) (2,3) (2,4)
(3,1) (3,2) (3,3) (3,4)
(4,1) (4,2) (4,3) (4,4)

The four qualifying outcomes are (1,4), (2,3), (3,2), (4,1). Thus P(sum=5) = 4/16 = 1/4. Distinguish ordered rolls; reversing different face values creates a different outcome.

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