Question

Given the following table of grades from Mrs. Hardcase's English classes:Write the notation, then answer as a fraction, decimal percent3. What is the probability that a randomly selected student got a A or B?4. What is the probability that an "A" student is male?P(male A)5. What is the probability that if a student was female that they got a passing grade?P(passing grade | female)6. What is the probability of a male student given that they failed?P()7. What is the probability of a randomly selected student is male?P()8. What is the probability of a female student given that they got a "B"?P()9. What is the probability of a randomly selected student passing Mrs. Hardcase's class PC)

Answer 1

• 3. 0.35

,

• 4. 0.6

,

• 5. 19/22

,

• 6. 7/13

,

• 7. 0.56

,

• 8. 0.6

,

• 9. 0.87

Explanation:

Part 3

The total number of students = 100

• The number of students who had a grade of A = 20

,

• The number of students who had a grade of B = 15

The probability that a randomly selected student got an A or B:

`P(A\text{ or B)=P(A)+P(B)}=(20)/(100)+(15)/(100)=(35)/(100)=0.35`

The probability that a randomly selected student got an A or B is 0.35.

Part 4

The number of male students who scored an A = 12.

`P(\text{male}|A)=\frac{P(\text{male and scored A)}}{P(scored\text{ A)}}=((12)/(100))/((20)/(100))=(12)/(20)=0.6`

The probability that an "A" student is male is 0.6.

Part 5

The passing grades are A, B, C, and D.

• The number of females who had a passing grade = 8+9+13+8 = 38

• The number of females = 44

`\begin{gathered} P(\textpassing grade\frac{\text{P(passing grade and female)}}{P(female)} \\ =(38)/(100)/(44)/(100) \\ =(38)/(44) \\ =(19)/(22) \end{gathered}`

The probability that if a student was female that they got a passing grade is 19/22.

Part 6

The probability of a male student given that they failed.

• The number of students who failed = 7+6 = 13

,

• The number of male students who failed = 7

`P(\textmale student=(7)/(13)`

The probability of a male student given that they failed is 7/13.

Part 7

• The total number of students = 100

,

• The number of male students = 56.

`P(\text{male)}=(56)/(100)=0.56`

The probability of a randomly selected student being male is 0.56.

Part 8

• The number of female students that got a B = 9.

,

• The number of students that got a B = 15

`P(\text{female}|B)=(9)/(15)=0.6`

The probability of a female student given that they got a "B" is 0.6.

Part 9

The number of students who passed Mrs. Hardcase's class = 100-13=87

`P(\text{passing)}=(87)/(100)=0.87`

The probability of a randomly selected student passing Mrs. Hardcase's class is 0.87.