What information can we obtain from the height of each bar on a histogram?
See solution.
Practice makes perfect
We want to find the probability of an event using a histogram. First, let's recall how to find the probability of an event X.
P(X) = Number of favorable outcomes/Total number of outcomes
Each bar on a histogram represents an event. The height of each bar indicates the number of favorable outcomes for the event. Therefore, to find the probability of an event, we divide the height of the bar by the sum of the heights of all of the bars. Let's look at an example!
Example
Suppose that we roll two dice and want to list the possible outcomes for the sum of the numbers rolled. Let's write these possibilities in a table.
Possible Rolls
Sum
Number of Outcomes
(1,1)
2
1
(1,2), (2,1)
3
2
(1,3), (2,2), (3,1)
4
3
(1,4), (2,3), (3,2), (4,1)
5
4
(1,5), (2,4), (3,3), (4,2), (5,1)
6
5
(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
7
6
(2,6), (3,5), (4,4), (5,3), (6,2)
8
5
(3,6), (4,5), (5,4), (6,3)
9
4
(4,6), (5,5), (6,4)
10
3
(5,6), (6,5)
11
2
(6,6)
12
1
We can make a histogram that displays this information. Each bar represents a sum of the numbers rolled. The height of each bar represents the number of outcomes that can make that sum. Let's draw a histogram!
Now, suppose that we want to find the probability that the sum of the rolled numbers is 8. Looking at the histogram, we can see that the height of the bar for that sum is 5. Adding the heights of all of the bars, we find that the total number of outcomes is 36. Let's find the probability!
P(8) = Number of favorable outcomes/Total number of outcomes
