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QuestionWhat is the probability that a randomly chosen student is not employed given they are job searching, based on the data? Express as a fraction.

Studdy Solution

STEP 1

Assumptions1. The total number of students surveyed is130. . The number of students who are employed and job searching is28.
3. The number of students who are employed and not job searching is61.
4. The number of students who are not employed and job searching is18.
5. The number of students who are not employed and not job searching is23.
6. The number of students who are job searching (employed or not) is46.
7. The number of students who are not job searching (employed or not) is84.
8. The number of employed students (job searching or not) is89.
9. The number of students who are not employed (job searching or not) is41.

STEP 2

We are asked to find the probability that a randomly chosen student is not employed given that they are job searching. This is a conditional probability problem. The formula for conditional probability is(A∣B)=(A∩B)(B)(A|B) = \frac{(A \cap B)}{(B)} Where- (A∣B)(A|B) is the probability of event A given event B. - (A∩B)(A \cap B) is the probability of both A and B occurring. - (B)(B) is the probability of event B.
In this case, event A is a student being not employed and event B is a student job searching.

STEP 3

First, we need to find (A∩B)(A \cap B), the probability of a student being not employed and job searching. We can find this by dividing the number of students who are not employed and job searching by the total number of students.
(A∩B)=Number of students not employed and job searchingTotal number of students(A \cap B) = \frac{Number\, of\, students\, not\, employed\, and\, job\, searching}{Total\, number\, of\, students}

STEP 4

Plug in the values for the number of students who are not employed and job searching and the total number of students to calculate (A∩B)(A \cap B).
(A∩B)=18130(A \cap B) = \frac{18}{130}

STEP 5

Next, we need to find (B)(B), the probability of a student job searching. We can find this by dividing the number of students who are job searching by the total number of students.
(B)=Number of students job searchingTotal number of students(B) = \frac{Number\, of\, students\, job\, searching}{Total\, number\, of\, students}

STEP 6

Plug in the values for the number of students who are job searching and the total number of students to calculate (B)(B).
(B)=46130(B) = \frac{46}{130}

STEP 7

Now that we have (A∩B)(A \cap B) and (B)(B), we can find (A∣B)(A|B), the probability of a student being not employed given that they are job searching, using the formula for conditional probability.
(A∣B)=(A∩B)(B)(A|B) = \frac{(A \cap B)}{(B)}

STEP 8

Plug in the values for (A∩B)(A \cap B) and (B)(B) to calculate (A∣B)(A|B).
(A∣B)=18/13046/130(A|B) = \frac{18/130}{46/130}

STEP 9

implify the fraction to find (A∣B)(A|B).
(A∣B)=1846(A|B) = \frac{18}{46} The probability that a randomly chosen student is not employed given that they are job searching is 1846\frac{18}{46}.

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