Three 6-sided dice are rolled simultaneously. What is the probability that no two dice display the same number__________?
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Answer: B. 5/9
Explanation
The total number of possible outcomes when rolling three six-sided dice is six cubed, or 216. The number of favorable outcomes where all three dice show distinct numbers is calculated as six times five times four. Dividing 120 favorable outcomes by 216 total outcomes and simplifying yields the fraction 5 over 9. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Multiplication principles of counting determine combinations of independent events without replacement. Fractions representing probabilities can be reduced to their simplest form by dividing by common factors.
Board games and casino simulations rely heavily on calculating probabilities of dice roll combinations. Statistical sampling techniques use combinations and permutations to analyze random event likelihoods. Understanding probability helps in evaluating risk and making informed decisions in uncertain scenarios. Option A overestimates the probability by using an incorrect count of favorable distinct outcomes. Option C represents a much lower probability that corresponds to rolling specific matching numbers rather than distinct ones. Option D underestimates the true fractional probability calculated from the combinatorial formula.
- Subject
- Mathematics
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- Mathematics
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- —
- Difficulty
- medium
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