Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, with adifferent number appearing on each face. Two such number cubes will be tossed, and the sum of the numbersappearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that thesum is less than or equal to 6
Question
Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, with adifferent number appearing on each face. Two such number cubes will be tossed, and the sum of the numbersappearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that thesum is less than or equal to 6
Solution
To solve this problem, we first need to understand the total possible outcomes when two dice are rolled. Since each die has 6 faces, the total possible outcomes are 6*6 = 36.
Next, we need to find out the possible outcomes that result in a sum of 4. They are (1,3), (2,2), and (3,1). So, there are 3 outcomes that result in a sum of 4.
Now, we need to find out the possible outcomes that result in a sum less than or equal to 6. They are (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (4,1), (4,2), (5,1), and (6,1). So, there are 16 outcomes that result in a sum less than or equal to 6.
The probability that the sum will be 4, given that the sum is less than or equal to 6, is the number of outcomes that result in a sum of 4 divided by the number of outcomes that result in a sum less than or equal to 6.
So, the probability = 3/16 = 0.1875 or 18.75%.
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