Probability Puzzles
Expert
3 min
Two fair dice are rolled. What is the probability that the first die is greater than the second die?
Hint
Use symmetry between the two dice.
Answer
5/12.
Explanation
There are 36 outcomes. Six are ties. The remaining 30 outcomes split equally between first-greater and second-greater, giving 15 favorable outcomes.
Step-by-Step Solution
Non-ties = 36 - 6 = 30.
Half = 15.
Probability = 15/36 = 5/12.
Half = 15.
Probability = 15/36 = 5/12.