SOLUTION: Given the following data for an imaginary superhero universe:
Flying Telepathy Super Strength
Female 98 58 49
Male 96 80 56
Distribution of Super Power by Gender
What
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-> SOLUTION: Given the following data for an imaginary superhero universe:
Flying Telepathy Super Strength
Female 98 58 49
Male 96 80 56
Distribution of Super Power by Gender
What
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Question 1167569: Given the following data for an imaginary superhero universe:
Flying Telepathy Super Strength
Female 98 58 49
Male 96 80 56
Distribution of Super Power by Gender
What is the empirical probability that a randomly selected female superhero will have Super Strength?
Answer in decimal form. Round to 3 decimal places as needed Answer by CPhill(1987) (Show Source):
You can put this solution on YOUR website! ```python?code_reference&code_event_index=2
# Data provided in the table for Female superheroes
female_flying = 98
female_telepathy = 58
female_super_strength = 49
# 1. Calculate the Total Number of Female Superheroes
total_female = female_flying + female_telepathy + female_super_strength
# 2. Identify the Number of Female Superheroes with Super Strength
female_super_strength_count = female_super_strength
# 3. Calculate the Empirical Conditional Probability: P(Super Strength | Female)
probability = female_super_strength_count / total_female
# Print results
print(f"Total Female Superheroes: {total_female}")
print(f"Female Super Strength Count: {female_super_strength_count}")
print(f"Probability (decimal): {probability}")
print(f"Probability (rounded to 3 decimal places): {probability:.3f}")
```
```text?code_stdout&code_event_index=2
Total Female Superheroes: 205
Female Super Strength Count: 49
Probability (decimal): 0.23902439024390243
Probability (rounded to 3 decimal places): 0.239
```
The empirical probability that a randomly selected **female** superhero will have **Super Strength** is **0.239**.
This is a **conditional probability** calculated as the ratio of female superheroes with Super Strength to the total number of female superheroes.
### Calculation Steps
1. **Total Number of Female Superheroes (Sample Space):**
$$\text{Total Female} = 98 (\text{Flying}) + 58 (\text{Telepathy}) + 49 (\text{Super Strength}) = 205$$
2. **Number of Female Superheroes with Super Strength (Event Count):**
$$\text{Female Super Strength} = 49$$
3. **Empirical Probability:**
$$P(\text{Super Strength} | \text{Female}) = \frac{\text{Female Super Strength}}{\text{Total Female}} = \frac{49}{205} \approx 0.23902...$$
Rounding to 3 decimal places gives **0.239**.
