Three 6-sided dice are rolled simultaneously. What is the probability that exactly two dice show matching numbers-.
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Answer: B. 5/12
Explanation
Rolling three six-sided dice generates a total sample space of two hundred sixteen possible outcome combinations. Counting all favorable outcomes where exactly two dice display matching numbers yields ninety possible ways. Dividing ninety favorable outcomes by the total two hundred sixteen outcomes simplifies to five over twelve. Probability is calculated as the number of favorable target outcomes divided by the total possible outcomes. Combinatorics principles count matching dice outcomes using permutations and combinations of face values. Simplifying probability fractions divides numerator and denominator by their greatest common divisor factor.
Probability analysts compute complex dice outcome distributions for tabletop game design and simulation. Statisticians use combinatorial probability models to evaluate random event likelihoods in gaming applications. Risk assessors calculate compound probability outcomes for quality control and reliability engineering tests. Option A suggests five over nine which overestimates the exact probability of two matching dice. Option C suggests one over thirty-six which represents the probability of all three dice matching instead. Option D suggests seven over twelve which incorrectly overcounts the favorable matching outcome combinations.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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