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QuestionGiven a group of students' grades and gender, find the following probabilities:
A. Probability student is male: B. Probability student is male AND got a "C": C. Probability student is male OR got a "C": D. Probability student is male GIVEN they got a 'C':
Use totals: Males = 37, Females = 23, Total = 60.

Studdy Solution

STEP 1

Assumptions1. The total number of students is60. . The number of male students is37.
3. The number of female students is23.
4. The number of students who got an 'A' is14.
5. The number of students who got a 'B' is32.
6. The number of students who got a 'C' is14.
7. The number of male students who got a 'C' is9.
8. The number of female students who got a 'C' is5.

STEP 2

A. To find the probability that the student was male, we divide the number of male students by the total number of students.
(Male)=Number of male studentsTotal number of students(Male) = \frac{Number\, of\, male\, students}{Total\, number\, of\, students}

STEP 3

Plug in the given values for the number of male students and the total number of students to calculate the probability.
(Male)=3760(Male) = \frac{37}{60}

STEP 4

Calculate the probability that the student was male.
(Male)=3760≈0.617(Male) = \frac{37}{60} \approx0.617

STEP 5

B. To find the probability that the student was male AND got a 'C', we divide the number of male students who got a 'C' by the total number of students.
(Male and C)=Number of male students who got a ′C′Total number of students(Male\, and\, C) = \frac{Number\, of\, male\, students\, who\, got\, a\, 'C'}{Total\, number\, of\, students}

STEP 6

Plug in the given values for the number of male students who got a 'C' and the total number of students to calculate the probability.
(Male and C)=960(Male\, and\, C) = \frac{9}{60}

STEP 7

Calculate the probability that the student was male and got a 'C'.
(Male and C)=960≈0.150(Male\, and\, C) = \frac{9}{60} \approx0.150

STEP 8

C. To find the probability that the student was male OR got a 'C', we add the probabilities of the two events and subtract the probability of both events occurring.
(Male or C)=(Male)+(C)−(Male and C)(Male\, or\, C) =(Male) +(C) -(Male\, and\, C)

STEP 9

First, we need to calculate the probability of getting a 'C'. This is done by dividing the total number of students who got a 'C' by the total number of students.
(C)=Number of students who got a ′C′Total number of students(C) = \frac{Number\, of\, students\, who\, got\, a\, 'C'}{Total\, number\, of\, students}

STEP 10

Plug in the given values for the number of students who got a 'C' and the total number of students to calculate the probability.
(C)=1460(C) = \frac{14}{60}

STEP 11

Calculate the probability of getting a 'C'.
(C)=1460≈0.233(C) = \frac{14}{60} \approx0.233

STEP 12

Now, plug in the calculated values for(Male),(C), and(Male and C) into the formula for(Male or C).
(Male or C)=0.617+0.233−0.150(Male\, or\, C) =0.617 +0.233 -0.150

STEP 13

Calculate the probability that the student was male or got a 'C'.
(Male or C)=0.617+0.233−0.150=0.700(Male\, or\, C) =0.617 +0.233 -0.150 =0.700

STEP 14

. To find the probability that the student was male GIVEN they got a 'C', we divide the number of male students who got a 'C' by the total number of students who got a 'C'.
(Male∣C)=Number of male students who got a ′C′Number of students who got a ′C′(Male | C) = \frac{Number\, of\, male\, students\, who\, got\, a\, 'C'}{Number\, of\, students\, who\, got\, a\, 'C'}

STEP 15

Plug in the given values for the number of male students who got a 'C' and the number of students who got a 'C' to calculate the probability.
(Male∣C)=914(Male | C) = \frac{9}{14}

STEP 16

Calculate the probability that the student was male given they got a 'C'.
(Male∣C)=914≈0.643(Male | C) = \frac{9}{14} \approx0.643So, the probabilities areA. The probability that the student was male is approximately0.617. B. The probability that the student was male and got a 'C' is approximately0.150. C. The probability that the student was male or got a 'C' is approximately0.700. . The probability that the student was male given they got a 'C' is approximately0.643.

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