Question

researchers surveyed one hundred students on which superpower they would most like to have. the two - way table below displays data for the sample of students who responded to the survey.
superpower | male | female | total
fly | 30 | 10 | 40
invisibility | 12 | 32 | 44
other | 10 | 6 | 16
total | 52 | 48 | 100
find the probability that the student was male, given the student chose to fly as their superpower.
$p(\text{male} | \text{fly}) = $

Explanation:

Step1: Recall conditional probability formula

The formula for conditional probability is \( P(A|B)=\frac{P(A\cap B)}{P(B)} \). In the context of a two - way table, if \( A \) is the event that the student is male and \( B \) is the event that the student chose to fly, then \( P(\text{male}|\text{fly})=\frac{\text{Number of students who are male and chose fly}}{\text{Number of students who chose fly}} \).

Step2: Identify the values from the table

From the two - way table, the number of students who are male and chose fly is 30, and the number of students who chose fly is 40.

Step3: Calculate the probability

Substitute the values into the formula: \( P(\text{male}|\text{fly})=\frac{30}{40}=\frac{3}{4} = 0.75 \)

Answer:

\( \frac{3}{4} \) (or 0.75)