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What is probability?
The study of chances
and predictions
Describes the likelihood of an event
Can you recall these?
- Trial: a single experiment
- Outcome: a possible result
- Event: a grouping of outcomes
Theoretical Probability
This type of probability describes the likelihood of an event to occur, given that the outcomes have even chances of occurring.
On a throw, getting either 1, 2, 3, 4, 5 or 6 is equally likely and can be calculated theoretically.
Calculating
Theoretical Probability
The formula below can be used to find the theoretical probability.
Theoretical
probability
Number of
favourable outcomes
Total number of
possible outcomes
Try this:
What is the theoretical probability of getting a 5 after a roll?
Calculating
Theoretical Probability
Using the formula
Theoretical
probability of getting 5
Number of
favourable outcomes
Total number of
possible outcomes
There is only one ‘5’.
1
6
1,2,3,4,5 or 6:
equally likely outcomes
This further tells that each number on the die has a theoretical probability of 1/6.
Experimental Probability
This type of probability describes the likeliness of an event to occur based on collected data.
For example, to get the experimental probability of getting a 5 after rolling it 100 times, it is a must to do the experiment to collect the data.
Experimental Probability
Inspect the results of the experiment.
Possible Outcomes | 1 | 2 | 3 | 4 | 5 | 6 |
Number of Times Obtained | 14 | 15 | 18 | 22 | 16 | 15 |
In the experiment,
5 was obtained 16 times.
Take Note:
The sum of these numbers is 100, the total number of rolls.
Calculating
Experimental Probability
The formula below can be used to find the experimental probability.
Experimental Probability
Number of times the event occurred
Total number of experiments / trials
So, what is the experimental probability of getting a 5?
Calculating
Experimental Probability
Using the formula
Experimental
probability of getting 5
Number of times the event occurred
Total number of rolls
Obtained from the data table
16
Refers to the total number of trials
100
This is equal to 16%.
Experimental probabilities may also be presented as percentages.
Experimental Probabilities
All the experimental probabilities for each outcome may be calculated using the formula.
Possible Outcomes | 1 | 2 | 3 | 4 | 5 | 6 |
Number of Times Obtained | 14 | 15 | 18 | 22 | 16 | 15 |
Experimental Probability | 14 100 | 15 100 | 18 100 | 22 100 | 16 100 | 15 100 |
Experimental Probability in % | 14% | 15% | 18% | 22% | 16% | 15% |
Theoretical vs. Experimental
Theoretical |
1 6 |
Number of
favourable outcomes
Total number of
possible outcomes
Outcomes are equally likely to occur
Can be calculated without an experiment
Do you notice the difference in the probabilities we calculated?
Experimental |
16 100 |
*or 16%
Number of times the event occurred
Total number of
trials
Outcomes may not be equally likely to occur
Must be obtained by gathering data from trials
Extend your learning!
It’s game day with friends!
Get yourselves a bag of a certain item with various colours.
Take turns selecting an item from the bag, record the colour of the object each of you have selected, and then return it before the next turn.
Calculate the theoretical and experimental probabilities of obtaining an object with a specific colour.
The person who arrives at the correct answer the fastest wins!
Resources
Educational Resources
Mathspace.
“15.03 Theoretical probability”
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