Suppose you roll two number cubes and find the probability distribution for the sum of the numbers. Which two sums have the same probability distribution and would be represented with equal bars on a bar graph?
The sum of two number cubes can range from 2 (when you roll two 1s) to 12 (when you roll two 6s). To find the probability distribution for the sum, we need to determine the number of ways each sum can occur and divide it by the total number of possible outcomes.
Let's construct a table to determine the probability distribution:
Sum | Number of Ways it Can Occur | Probability
---|---|---
2 | 1 | 1/36
3 | 2 | 2/36
4 | 3 | 3/36
5 | 4 | 4/36
6 | 5 | 5/36
7 | 6 | 6/36
8 | 5 | 5/36
9 | 4 | 4/36
10 | 3 | 3/36
11 | 2 | 2/36
12 | 1 | 1/36
Now let's analyze the table to find the sums with the same probability distribution. We can see that the sums 2 and 12 have the same probability distribution, as they both have 1 way to occur and a probability of 1/36. Additionally, the sums 3 and 11, 4 and 10, 5 and 9, and 6 and 8 also have the same probability distribution. These pairs would be represented with equal bars on a bar graph.