Question

A researcher at a large university wanted to investigate if a student's seat preference was related in any way to the gender of the student. The researcher divided the lecture room into 3 zones:front center, front sides, and back of the classroom. He noted where his students sat on a particular day of the class and summarized the data below.BackFront Center1510Sides71011Total333972MalesFemalesTotal19251730Suppose a student is selected at random. Find the probability that the student was a Female, given they sat in the Front Center of the classroom8. P(Female, given Sides of the room) -

Answer 1

To find the probability you use the next:

For probability of A given B

`P(A|B)=(P(A\cap B))/(P(B))`

For the given situation:

Find the probability that the student was a Female, given they sat in the Front Center of the classroom

A = Female student

B = Sat in the front center

1. Find P( A∩B). number of female students sat in front center (10) divided into the total number of stuents (72)

`P(A\cap B)=(10)/(72)`

2. Find the probability of B (P(B)). Number of students sat in the front center (25) divided into the total number of students(72):

`P(B)=(25)/(72)`

3. Find the probability of A given B:

`P(A|B)=((10)/(72))/((25)/(72))=(10)/(25)=0.4`Then, the probability taht the studen was female, given they sat in the front center of the classroom is 0.4 (or 40%)