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?

We want to get the probability of getting a sum of 4, given that the sum is less than or equal to 6. We will see that the probability is 0.2

We need to get the total number of outcomes such that the sum is equal or smaller than 6, and also get the total number of outcomes such that the sum is equal to 4.

The sum is 6 if the outcomes are:

dice 1   dice 2

2             4

4             2

5             1

1               5

3             3

So we have 5 outcomes.

The sum is 5 if the outcomes are:

dice 1   dice 2

1             4

4             1

2             3

3              2

Here we have 4 outcomes

The sum is 4 if the outcomes are:

dice 1   dice 2

1             3

3             1

2             2

So there are 3 outcomes.

The sum is 3 if the outcomes are:

dice 1   dice 2

1             2

2             1

So here we have 2 outcomes

The sum is 2 if the outcomes are:

dice 1   dice 2

1            1

So here we have only one outcome.

Adding all of these, the total outcomes with a sum equal or smaller than 6 is:

5 + 4 + 3 + 2 + 1 = 15

And the outcomes with a sum equal to 4 are 3, then the probability of getting a sum of 4, given that the sum is less than or equal to 6 is just the quotient between the numbers of outcomes:

P = 3/15 = 0.2

If you want to learn more about probability, you can read:

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0.2 = 20%

Step-by-step explanation:

The possibilities that give us a sum of 6 or less 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)

(Total of 15 possibilities)

The possibilities that have a sum of 4 are:

(1,3), (2,2), (3,1)

(Total of 3 possibilities)

So, the probability that the sum will be 4, given that the sum is less than or equal to 6 is:

P = 3/15 = 0.2 = 20%

17 1/3

step-by-step explanation: