A pair of dice is tossed twice.Find the probability that both rolls give a sum of 5. (Enter your probability as a fraction.)
Question
A pair of dice is tossed twice. Find the probability that both rolls give a sum of 5. (Enter your probability as a fraction.)
Solution
To solve this problem, we first need to understand the total number of outcomes when a pair of dice is rolled. Since each die has 6 faces, the total number of outcomes when two dice are rolled is 6*6 = 36.
Next, we need to find out the number of outcomes that give a sum of 5. These are: (1,4), (2,3), (3,2), (4,1). So, there are 4 outcomes that give a sum of 5.
Therefore, the probability of getting a sum of 5 when a pair of dice is rolled is 4/36 = 1/9.
Since the pair of dice is tossed twice, we need to find the probability of getting a sum of 5 in both tosses. The probability of two independent events both happening is the product of their individual probabilities.
So, the probability that both rolls give a sum of 5 is (1/9) * (1/9) = 1/81.
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