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QuestionA university has 22,028 students. Find these probabilities: a) Off-campus or junior. b) On-campus and senior. c) Freshman given on-campus. Use fractions or decimals rounded to three places.

Studdy Solution

STEP 1

Assumptions1. The total number of students is22028. . The number of students who live off campus is13714.
3. The number of students who are juniors is7526.
4. The number of students who live on campus and are seniors is637.
5. The number of students who live on campus is8314.
6. The number of students who are freshmen and live on campus is1560.

STEP 2

To find the probability that a student lives off campus or is a junior, we first need to find the total number of students who either live off campus or are juniors. We can do this by adding the number of students who live off campus to the number of juniors. However, we must be careful not to double count students who are juniors and live off campus.
(Off Campus or Junior)=Number of Off Campus Students+Number of Juniors−Number of Juniors living Off CampusTotal Number of Students(\text{{Off Campus or Junior}}) = \frac{{\text{{Number of Off Campus Students}} + \text{{Number of Juniors}} - \text{{Number of Juniors living Off Campus}}}}{{\text{{Total Number of Students}}}}

STEP 3

Plug in the given values to calculate the probability.
(Off Campus or Junior)=13714+7526−430022028(\text{{Off Campus or Junior}}) = \frac{{13714 +7526 -4300}}{{22028}}

STEP 4

Calculate the probability that a student lives off campus or is a junior.
(Off Campus or Junior)=1694022028(\text{{Off Campus or Junior}}) = \frac{{16940}}{{22028}}

STEP 5

To find the probability that a student lives on campus and is a senior, we divide the number of students who live on campus and are seniors by the total number of students.
(On Campus and Senior)=Number of Seniors living On CampusTotal Number of Students(\text{{On Campus and Senior}}) = \frac{{\text{{Number of Seniors living On Campus}}}}{{\text{{Total Number of Students}}}}

STEP 6

Plug in the given values to calculate the probability.
(On Campus and Senior)=63722028(\text{{On Campus and Senior}}) = \frac{{637}}{{22028}}

STEP 7

Calculate the probability that a student lives on campus and is a senior.
(On Campus and Senior)=63722028(\text{{On Campus and Senior}}) = \frac{{637}}{{22028}}

STEP 8

To find the probability that a student is a freshman given that they live on campus, we divide the number of students who are freshmen and live on campus by the total number of students who live on campus.
(Freshman | On Campus)=Number of Freshmen living On CampusTotal Number of On Campus Students(\text{{Freshman | On Campus}}) = \frac{{\text{{Number of Freshmen living On Campus}}}}{{\text{{Total Number of On Campus Students}}}}

STEP 9

Plug in the given values to calculate the probability.
(Freshman | On Campus)=1568314(\text{{Freshman | On Campus}}) = \frac{{156}}{{8314}}

STEP 10

Calculate the probability that a student is a freshman given that they live on campus.
(Freshman | On Campus)=15608314(\text{{Freshman | On Campus}}) = \frac{{1560}}{{8314}}a) The probability that the student lives off campus or is a junior is approximately0.769. b) The probability that the student lives on campus and is a senior is approximately0.029. c) The probability that the student is a freshman given that they live on campus is approximately0.188.

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