Three 6-sided dice are rolled simultaneously. What is the probability that all three display the same number-.
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Answer: B. 1/36
Explanation
Rolling three six-sided dice simultaneously produces a total sample space of two hundred sixteen outcomes. The number of favorable outcomes where all three dice show identical numbers is exactly six possible ways. Dividing the six favorable outcomes by the total two hundred sixteen outcomes simplifies to one over thirty-six. Probability equals the number of favorable outcomes divided by the total number of possible outcomes. The total outcome count for multiple dice equals six raised to the power of the number of dice rolled. Simplifying probability fractions involves dividing numerator and denominator by their greatest common divisor.
Probability theorists calculate complex dice roll combinations when analyzing tabletop board game mechanics. 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 one over two hundred sixteen which represents the probability of one specific exact triple outcome. Option C suggests five over nine which grossly overestimates the likelihood of rolling identical numbers. Option D suggests five over twelfth which is mathematically incorrect for three independent dice rolls.
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