5. Adding Probabilities
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The result of how many spins are summarized in the table?
Make sure to use the correct height for the bars.
Why is it important that the sections of the spinner are of equal size?
Make sure to use the correct height for the bars.
Are the two graphs a close match?
Experimental probabilities:
| Color | Frequency | Experimental Probability |
|---|---|---|
| red | 6 | 6/50=0.12 |
| blue | 7 | 7/50=0.14 |
| yellow | 9 | 9/50=0.18 |
| orange | 12 | 12/50=0.24 |
| purple | 5 | 5/50=0.1 |
| green | 11 | 11/50=0.22 |
Bar chart:
Theoretical probabilities:
| Color | Frequency | Experimetal Probability | Theoretical Probability |
|---|---|---|---|
| red | 6 | 0.12 | 1/6=0.16 |
| blue | 7 | 0.14 | 1/6=0.16 |
| yellow | 9 | 0.18 | 1/6=0.16 |
| orange | 12 | 0.24 | 1/6=0.16 |
| purple | 5 | 0.1 | 1/6=0.16 |
| green | 11 | 0.22 | 1/6=0.16 |
Bar Chart:
See solution.
We want to find the probability of landing on each color of the spinner. The experimental probability is a quotient.
P(E)=number of favorable trials/number of trials
| Color | Frequency | Experimental Probability |
|---|---|---|
| red | 6 | 6/50= 0.12 |
| blue | 7 | 7/50= 0.14 |
| yellow | 9 | 9/50= 0.18 |
| orange | 12 | 12/50= 0.24 |
| purple | 5 | 5/50= 0.1 |
| green | 11 | 11/50= 0.22 |
Let's now plot these values on a bar graph. The height of the bars should be proportional to the probabilities we found in part A.
Since the spinner has sections of equal size, let's assume that landing on different colors is equally likely. Under this assumption, the theoretical probability can be calculated as a quotient.
| Color | Frequency | Experimetal Probability | Theoretical Probability |
|---|---|---|---|
| red | 6 | 0.12 | 1/6= 0.16 |
| blue | 7 | 0.14 | 1/6= 0.16 |
| yellow | 9 | 0.18 | 1/6= 0.16 |
| orange | 12 | 0.24 | 1/6= 0.16 |
| purple | 5 | 0.1 | 1/6= 0.16 |
| green | 11 | 0.22 | 1/6= 0.16 |
Let's now graph the theoretical probability. The height of the bars should be proportional to the probabilities we found in part C.
The bars on the graph of the theoretical probability are of equal height. This is the consequence of our assumption, that landing on different colors is equally likely.