Ben rolls two number cubes. What is the probability that the sum of the numbers he rolls is less than 6
To find the probability that the sum of the numbers Ben rolls is less than 6, we need to calculate the favorable outcomes divided by the total outcomes.
Let's list all the possible outcomes for rolling two number cubes:
1 + 1 = 2
1 + 2 = 3
1 + 3 = 4
1 + 4 = 5
1 + 5 = 6
1 + 6 = 7
2 + 1 = 3
2 + 2 = 4
2 + 3 = 5
2 + 4 = 6
2 + 5 = 7
2 + 6 = 8
3 + 1 = 4
3 + 2 = 5
3 + 3 = 6
3 + 4 = 7
3 + 5 = 8
3 + 6 = 9
4 + 1 = 5
4 + 2 = 6
4 + 3 = 7
4 + 4 = 8
4 + 5 = 9
4 + 6 = 10
5 + 1 = 6
5 + 2 = 7
5 + 3 = 8
5 + 4 = 9
5 + 5 = 10
5 + 6 = 11
6 + 1 = 7
6 + 2 = 8
6 + 3 = 9
6 + 4 = 10
6 + 5 = 11
6 + 6 = 12
From the outcomes listed, we can see that there are 10 favorable outcomes (sums less than 6: 2, 3, 4, 5) out of 36 total outcomes.
Therefore, the probability that the sum of the numbers Ben rolls is less than 6 is 10/36 or simplified as 5/18.
To find the probability that the sum of the numbers Ben rolls is less than 6, we need to determine the number of favorable outcomes (where the sum is less than 6) and the number of possible outcomes.
Let's first list all possible outcomes when rolling two number cubes. Each cube has 6 sides with numbers 1 through 6.
Possible outcomes for the first number cube (Cube 1):
1, 2, 3, 4, 5, 6
Possible outcomes for the second number cube (Cube 2):
1, 2, 3, 4, 5, 6
Now, we will find the favorable outcomes, where the sum is less than 6. We can do this by listing all the pairs of numbers whose sum is less than 6.
Favorable outcomes:
(1, 1), (1, 2), (1, 3), (1, 4)
(2, 1), (2, 2), (2, 3)
(3, 1), (3, 2)
(4, 1)
Counting the favorable outcomes, we find that there are 10 of them.
Next, let's calculate the total number of possible outcomes by multiplying the number of outcomes for each cube together. Since each cube has 6 possible outcomes, the total number of outcomes is 6 × 6 = 36.
Finally, we can determine the probability by dividing the number of favorable outcomes (10) by the number of possible outcomes (36):
Probability = Favorable outcomes / Total outcomes
Probability = 10 / 36
Probability = 5 / 18
Therefore, the probability that the sum of the numbers Ben rolls is less than 6 is 5/18.
how many rolls add up to 2,3,4,5?
There are 36 possible rolls.