A test was given to a group of students. The grades and gender are summarized below A C Total Male 8. 11 9. 28 Female 20 18 12 50 Total 28 29 21 78 If one student is chosen at random from those who took the test, Find the probability that the student was female GIVEN they got a 'B'.

A test was given to a group of students. The grades and gender are summarized below A C Total Male 8. 11 9. 28 Female 20 18 12 50 Total 28 29 21 78 If one student is chosen at random from those who took the test, Find the probability that the student was female GIVEN they got a 'B'.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

A test was given to a group of students. The grades and gender are summarized below:

```
A B C Total
Male 8 11 9 28
Female 20 18 12 50
Total 28 29 21 78
```

If one student is chosen at random from those who took the test, find the probability that the student was female GIVEN they got a 'B'.

Expert Solution

Step 1

To calculate:

Probability that the student was female given that they got a B.

Using Conditional probability,

$P (f e m a l e | G o t B) = \frac{P (f e m a l e \cap G o t B)}{P (G o t B)}$

Number of females who got B grade = 18

Total number of students who got B grade = 29

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