Two dice are rolled. Determine the probability of the following. ("Doubles" means both dice show the same number. Enter your probabilities as fractions.)(a)rolling an even sum
Question
Two dice are rolled. Determine the probability of the following. ("Doubles" means both dice show the same number. Enter your probabilities as fractions.)(a)rolling an even sum
Solution
To solve this problem, we first need to understand the total number of possible outcomes when two dice are rolled. Since a die has 6 faces, the total number of outcomes is 6*6 = 36.
(a) To find the probability of rolling an even sum, we need to find all the outcomes where the sum of the numbers on the two dice is even. The pairs that satisfy this condition are (1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5), (4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6). That's a total of 18 pairs.
So, the probability of rolling an even sum is the number of favorable outcomes divided by the total number of outcomes, which is 18/36 = 1/2.
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