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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) -

A researcher at a large university wanted to investigate if a students seat preference was related in any way to the gender of the student The researcher divide class=

Respuesta :

To find the probability you use the next:

For probability of A given B

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

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)

[tex]P(A\cap B)=\frac{10}{72}[/tex]

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):

[tex]P(B)=\frac{25}{72}[/tex]

3. Find the probability of A given B:

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

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