A game involves rolling a fair four-sided die and a fair six-sided die together. What is the probability that the sum of the two dice is odd?

Instruction: Roll independent fair dice numbered 1–4 and 1–6. Describe the 24-outcome sample space, list the favorable pairs, and use parity to check the probability of an odd sum.

Context: This question tests the candidate's ability to understand and calculate probabilities involving multiple dice with different numbers of sides.

Updated

Official answer

An odd sum requires one odd face and one even face. Assume the two fair dice are independent, numbered 1–4 and 1–6. There are 24 equally likely ordered outcomes. The twelve qualifying pairs are:

(1,2) (1,4) (1,6)
(2,1) (2,3) (2,5)
(3,2) (3,4) (3,6)
(4,1) (4,3) (4,5)

Thus P(odd sum) = 12/24 = 1/2. The parity calculation agrees: (2/4)(3/6)+(2/4)(3/6)=1/2. The two cases are disjoint, so their probabilities add.

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