5. Adding Probabilities
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| 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 |
| 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 |
For the different colors the number of favorable trials is given in the table. The total number of trials is the sum of these individual frequencies. 6+ 7+ 9+ 12+ 5+ 11= 50 Let's find these quotients and add a column to the table as asked.
| 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 |
P(E)=number of favorable outcomes/number of possible outcomes In this case, the number of possible outcomes is the number of colors, so it is 6. For calculating the probability of the spinner landing on each color, the number of favorable outcomes is 1. Let's add these theoretical probabilities to the table.
| 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 |
The bars on the graph of the experimental probabilities are not of equal height. This indicates that the assumption of the uniform distribution may not be justified.