If you roll four six-sided dice, what is the probability that at least two dice will land on the same number?

Instruction: Assume four independent fair dice numbered 1–6. Use the complement of all four values being different to calculate the probability of at least one match.

Context: This question assesses the candidate's ability to understand and apply the concept of complementary probability to calculate the likelihood of an event.

Updated

Official answer

Assume four independent fair six-sided dice. All four values are different in 6×5×4×3=360 of the 6^4=1296 equally likely ordered outcomes.

Thus P(all different)=360/1296=5/18, and P(at least one match)=1−5/18=13/18, about 72.22%.

The product (6/6)(5/6)(4/6)(3/6) equals 5/18, not 5/54. “At least two match” includes a single pair, two pairs, triples and four equal dice; the complement avoids double-counting those cases.

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