Flavia tossed two six-sided number cubes and added the numbers together. Which outcomes have a probability of 1/12? Select two answers.
A. 3****
B. 4
C. 5
D. 7
E. 10***
To find the outcomes that have a probability of 1/12 when two six-sided number cubes are tossed and the numbers are added together, we need to determine which sums have a total of 12 possible outcomes (since the total number of possible outcomes when two six-sided number cubes are tossed is 36).
The possible outcomes for each roll of the number cube are 1, 2, 3, 4, 5, and 6.
To determine the sums, we can create a table with all possible combinations of two numbers from 1 to 6 and calculate their sums:
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 this table, we can see that the sums of 3 and 10 each appear only once out of the 12 possible outcomes.
Therefore, the outcomes that have a probability of 1/12 are:
A. 3
E. 10
To find the outcomes with a probability of 1/12 when tossing two six-sided number cubes and adding the numbers together, we need to determine the possible sums and their corresponding probabilities.
First, let's find all possible sums:
- When rolling a six-sided number cube, the possible outcomes are 1, 2, 3, 4, 5, and 6.
- By adding the numbers together, the possible sums are: 1+1=2, 1+2=3, 1+3=4, 1+4=5, 1+5=6, 1+6=7, 2+2=4, 2+3=5, 2+4=6, 2+5=7, 2+6=8, 3+3=6, 3+4=7, 3+5=8, 3+6=9, 4+4=8, 4+5=9, 4+6=10, 5+5=10, 5+6=11, 6+6=12.
Next, let's find the probability of each sum:
- Since there are 36 possible outcomes (6 possible outcomes on each of the two number cubes), we divide 1 by 36 to find the probability of each specific sum.
Now, let's determine the outcomes with a probability of 1/12:
- By multiplying the probability of 1/36 with the number of outcomes for each sum, we find that the sums 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 each have a probability of 1/12.
- Therefore, the outcomes with a probability of 1/12 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
Looking at the answer choices, the outcomes with a probability of 1/12 are:
A. 3
E. 10
A is wrong. 3 only occurs 2 out of 36 ways
E is ok
now check the others.