Question 1167570: Given the following data for an imaginary superhero universe:
Flying Telepathy Super Strength
Female 89 46 12
Male 35 38 82
Distribution of Super Power by Gender
What is the empirical probability that a randomly selected 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
data = {
'Female': {'Flying': 89, 'Telepathy': 46, 'Super Strength': 12},
'Male': {'Flying': 35, 'Telepathy': 38, 'Super Strength': 82}
}
# 1. Calculate Total Superheroes
total_female = sum(data['Female'].values())
total_male = sum(data['Male'].values())
total_superheroes = total_female + total_male
# 2. Calculate Total Superheroes with Super Strength
total_super_strength = data['Female']['Super Strength'] + data['Male']['Super Strength']
# 3. Calculate Empirical Probability of Super Strength
probability_super_strength = total_super_strength / total_superheroes
# Print results
print(f"Total Superheroes: {total_superheroes}")
print(f"Total Super Strength Superheroes: {total_super_strength}")
print(f"Probability of Super Strength (decimal): {probability_super_strength}")
print(f"Probability of Super Strength (rounded to 3 decimal places): {probability_super_strength:.3f}")
```
```text?code_stdout&code_event_index=2
Total Superheroes: 302
Total Super Strength Superheroes: 94
Probability of Super Strength (decimal): 0.31125827814569534
Probability of Super Strength (rounded to 3 decimal places): 0.311
```
The empirical probability that a randomly selected superhero will have **super strength** is **0.311**.
This is calculated as the ratio of the total number of superheroes with super strength to the total number of superheroes.
### Calculation Steps
1. **Total Super Strength Superheroes:**
$$\text{Total Super Strength} = \text{Female} + \text{Male} = 12 + 82 = 94$$
2. **Total Superheroes (Sample Size):**
$$\begin{aligned} \text{Total Superheroes} &= (\text{Female Total}) + (\text{Male Total}) \\ &= (89 + 46 + 12) + (35 + 38 + 82) \\ &= 147 + 155 \\ &= 302 \end{aligned}$$
3. **Empirical Probability:**
$$P(\text{Super Strength}) = \frac{\text{Total Super Strength}}{\text{Total Superheroes}} = \frac{94}{302} \approx 0.311258...$$
Rounding to 3 decimal places gives **0.311**.
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