Question 1167571: Given the following data for an imaginary superhero universe:
Flying Telepathy Super Strength
Female 78 24 7
Male 83 40 46
Distribution of Super Power by Gender
What is the empirical probability that a randomly selected superhero will have telepathy?
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': 78, 'Telepathy': 24, 'Super Strength': 7},
'Male': {'Flying': 83, 'Telepathy': 40, 'Super Strength': 46}
}
# 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 Telepathy
total_telepathy = data['Female']['Telepathy'] + data['Male']['Telepathy']
# 3. Calculate Empirical Probability of Telepathy
probability_telepathy = total_telepathy / total_superheroes
# Print results
print(f"Total Superheroes: {total_superheroes}")
print(f"Total Telepathy Superheroes: {total_telepathy}")
print(f"Probability of Telepathy (decimal): {probability_telepathy}")
print(f"Probability of Telepathy (rounded to 3 decimal places): {probability_telepathy:.3f}")
```
```text?code_stdout&code_event_index=2
Total Superheroes: 278
Total Telepathy Superheroes: 64
Probability of Telepathy (decimal): 0.2302158273381295
Probability of Telepathy (rounded to 3 decimal places): 0.230
```
The empirical probability that a randomly selected superhero will have telepathy is calculated by dividing the total number of superheroes with telepathy by the total number of superheroes.
### 1\. Calculate the Total Number of Superheroes
$$\begin{aligned} \text{Total Superheroes} &= \text{Total Female} + \text{Total Male} \\ &= (78 + 24 + 7) + (83 + 40 + 46) \\ &= 109 + 169 \\ &= 278 \end{aligned}$$
### 2\. Calculate the Total Number of Superheroes with Telepathy
$$\begin{aligned} \text{Total Telepathy} &= \text{Female Telepathy} + \text{Male Telepathy} \\ &= 24 + 40 \\ &= 64 \end{aligned}$$
### 3\. Calculate the Empirical Probability
$$\begin{aligned} P(\text{Telepathy}) &= \frac{\text{Total Telepathy}}{\text{Total Superheroes}} \\ &= \frac{64}{278} \\ &\approx 0.230215...\end{aligned}$$
Rounding to 3 decimal places gives **0.230**.
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