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

Answer:

• 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:

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

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.

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

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

$\begin{gathered} P(\text{passing grade|female)=}\frac{\text{P(passing grade and female)}}{P(female)} \\ =\frac{38}{100}\div\frac{44}{100} \\ =\frac{38}{44} \\ =\frac{19}{22} \end{gathered}$

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

$P(\text{male student|failed)}=\frac{7}{13}$

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.

$P(\text{male)}=\frac{56}{100}=0.56$

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

$P(\text{female}|B)=\frac{9}{15}=0.6$

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

$P(\text{passing)}=\frac{87}{100}=0.87$

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