The following table shows free throws. shot by a basicethall player. Explain why the empirical and theiretical probabilities are differentr outcome frequency empirical theore tical missed made 4 O.20 0.10 16 0.80 0,90 20 1.00 100

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The following text and table provide information on free throws shot by a basketball player. It explores the difference between empirical and theoretical probabilities.

**Text:**

The following table shows free throws shot by a basketball player. Explain why the empirical and theoretical probabilities are different.

**Table:**

| Outcome | Frequency | Empirical Probability | Theoretical Probability |
|---------|-----------|-----------------------|-------------------------|
| Missed  | 4         | 0.20                  | 0.10                    |
| Made    | 16        | 0.80                  | 0.90                    |
| Total   | 20        | 1.00                  | 1.00                    |

**Explanation:**

1. **Outcome:** The possible results of the free throw – either Missed or Made.

2. **Frequency:** The actual count of each outcome – 4 misses and 16 makes out of 20 free throws.

3. **Empirical Probability:** Calculated from actual data – the probability of missing is 0.20 (4/20) and making is 0.80 (16/20).

4. **Theoretical Probability:** Expected probabilities based on assumptions – the probability of missing is 0.10 and making is 0.90.

**Discussion:**

Empirical probabilities are based on real-world results from a specific set of data, while theoretical probabilities are calculated based on expected outcomes under ideal conditions. Differences between them can occur due to sample size, variability, and real-world factors not accounted for in theoretical models.
Transcribed Image Text:The following text and table provide information on free throws shot by a basketball player. It explores the difference between empirical and theoretical probabilities. **Text:** The following table shows free throws shot by a basketball player. Explain why the empirical and theoretical probabilities are different. **Table:** | Outcome | Frequency | Empirical Probability | Theoretical Probability | |---------|-----------|-----------------------|-------------------------| | Missed | 4 | 0.20 | 0.10 | | Made | 16 | 0.80 | 0.90 | | Total | 20 | 1.00 | 1.00 | **Explanation:** 1. **Outcome:** The possible results of the free throw – either Missed or Made. 2. **Frequency:** The actual count of each outcome – 4 misses and 16 makes out of 20 free throws. 3. **Empirical Probability:** Calculated from actual data – the probability of missing is 0.20 (4/20) and making is 0.80 (16/20). 4. **Theoretical Probability:** Expected probabilities based on assumptions – the probability of missing is 0.10 and making is 0.90. **Discussion:** Empirical probabilities are based on real-world results from a specific set of data, while theoretical probabilities are calculated based on expected outcomes under ideal conditions. Differences between them can occur due to sample size, variability, and real-world factors not accounted for in theoretical models.
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