decimal places. Grades and Gender A B C Total Male 13 17 6 36 Female 19 9. 33 Total 32 22 15 69 If one student is chosen at random, a. Find the probability that the student got an A: b. Find the probability that the student was male AND got a "B": c. Find the probability that the student was male OR got a "C":

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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**Probability and Statistics: An Example Study**

In this exercise, we examine a dataset representing the grades of students based on gender. Here is the summarized data:

| Grades and Gender |  A  |  B  |  C  | Total |
|-------------------|----|----|----|-------|
| Male              | 13 | 17 |  6 |    36  |
| Female            | 19 |  5 |  9 |    33  |
| Total             | 32 | 22 | 15 |    69  |

**Analyzing the Data**

From this table, we can evaluate different probabilities related to the students' grades:

a. **Probability of Getting an A**

   Calculate the probability that if one student is chosen at random, they received an 'A'.

b. **Probability of Being Male and Getting a B**
   
   Calculate the probability that a randomly selected student is both male and received a 'B'.

c. **Probability of Being Male or Getting a C**

   Determine the probability that a student is either male or received a 'C'.

d. **Probability of Getting a C Given the Student is Female**

   If one student is chosen at random, calculate the probability that the student received a 'C', given that they are female.

These calculations introduce students to the concept of conditional probability and how it intersects with other probability principles. By using real data, students can see how mathematical theories apply to practical situations.
Transcribed Image Text:**Probability and Statistics: An Example Study** In this exercise, we examine a dataset representing the grades of students based on gender. Here is the summarized data: | Grades and Gender | A | B | C | Total | |-------------------|----|----|----|-------| | Male | 13 | 17 | 6 | 36 | | Female | 19 | 5 | 9 | 33 | | Total | 32 | 22 | 15 | 69 | **Analyzing the Data** From this table, we can evaluate different probabilities related to the students' grades: a. **Probability of Getting an A** Calculate the probability that if one student is chosen at random, they received an 'A'. b. **Probability of Being Male and Getting a B** Calculate the probability that a randomly selected student is both male and received a 'B'. c. **Probability of Being Male or Getting a C** Determine the probability that a student is either male or received a 'C'. d. **Probability of Getting a C Given the Student is Female** If one student is chosen at random, calculate the probability that the student received a 'C', given that they are female. These calculations introduce students to the concept of conditional probability and how it intersects with other probability principles. By using real data, students can see how mathematical theories apply to practical situations.
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