To calculate the probabilities for each number chosen (1 to 5), you'll use the formula for probability:
\[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the total number of people surveyed is 100.
a) Probabilities:
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Probability that the number chosen is 1:
- Number who chose 1: 15 \[ P(1) = \frac{15}{100} = 0.15 \]
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Probability that the number chosen is 2:
- Number who chose 2: 26 \[ P(2) = \frac{26}{100} = 0.26 \]
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Probability that the number chosen is 3:
- Number who chose 3: 21 \[ P(3) = \frac{21}{100} = 0.21 \]
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Probability that the number chosen is 4:
- Number who chose 4: 22 \[ P(4) = \frac{22}{100} = 0.22 \]
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Probability that the number chosen is 5:
- Number who chose 5: 16 \[ P(5) = \frac{16}{100} = 0.16 \]
Summary of probabilities:
- \( P(1) = 0.15 \)
- \( P(2) = 0.26 \)
- \( P(3) = 0.21 \)
- \( P(4) = 0.22 \)
- \( P(5) = 0.16 \)
b) General Conclusion:
From the results, it can be observed that the distribution of choices is not uniform. The number 2 was the most commonly chosen option, while the number 1 was the least commonly chosen among the options. This suggests that certain numbers may be perceived as more favorable or appealing than others in this range. Additionally, the probabilities indicate that individuals have preferences that are not evenly distributed across the choices.