You are given two dice. Determine the probability of one of the faces being 3 and  the probability of the sum being divisible by 4.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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Each die has has 6 faces with numbers from 1 to 6. The set of the numbers that can show up on each die is {1, 2, 3, 4, 5, 6}

When 2 dice are thrown the probability of any one of the faces being 3 is 1/6 + 1/6 = 2/6 = 1/3

The sum of the number that shows up on each of the two dice is divisible by 4 if either each of the numbers is divisible by 2 or any one of them is divisible by 2. The probability of the number on each die being divisible by 2 is (1/2)*(1/2) = 1/4. The probability of any one of the numbers being divisible by 4 is 2*(1/6) = 1/3. Adding the two, the probaility that the sum is divisible by 4 is 7/12

The probability of one of the faces being 3 is 1/3 and the probability that the sum is divisible by 4 is 7/12.

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