Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, with a different number appearing on each face. Two such number cubes will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that the sum 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 a different number appearing on each face. Two such number cubes will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that the sum is less than or equal to 6 ?
Solution
To solve this problem, we need to first find out all the possible outcomes when two dice are rolled and the sum is less than or equal to 6. Then, we need to find out the outcomes where the sum is exactly 4. The probability will be the ratio of these two numbers.
Step 1: Find all possible outcomes when two dice are rolled and the sum is less than or equal to 6.
The possible outcomes 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). So, there are 15 possible outcomes.
Step 2: Find all possible outcomes where the sum is exactly 4.
The possible outcomes are: (1,3), (2,2), (3,1). So, there are 3 possible outcomes.
Step 3: Calculate the probability.
The probability is the number of favorable outcomes divided by the total number of outcomes. So, the probability that the sum will be 4, given that the sum is less than or equal to 6 is 3/15 = 1/5 = 0.2 or 20%.
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