Question

14. Two fair dice are thrown. What is the probability of at least one odd number? What is the probability of this if four fair dice are thrown?

Answer 1

When we roll a pair of fair dice the possible sample space is

Out of 36 outcomes, 27 outcomes shows at least one odd so the probability of at least one odd number is

P(at least one odd number) = 27 /36 = 0.75

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When four dice are rolled possible number of outcomes are 6*6*6*6 = 1296

When a single die is rolled possible outcomes are 1, 2, 3, 4, 5, and 6. Out of 6 possible outcomes 3 are odd and 3 are even.

Let us find the number of outcomes out of 1296 outcomes that have only even numbers. That is each dice can take 3 outcomes so possible number of outcomes with all even numbers is

3*3*3*3 = 81

Therefore number of outcomes with at least one odd is 1296 - 81 = 1215

The required probability is

1215 /1296 = 0.9375