Question

one hundred upper - division students attending a career fair at a university were categorized according to class and according to primary career motivation. the table shows the results. if one of these students is to be selected at random, find the probability that the student selected is a junior, given that their primary motivation is money.

|primary career motivation|
|----|

money

allowed to be creative

sense of giving to society

total

|----|

junior	9	6	9	24
senior	22	25	29	76
total	31	31	38	100

the probability that the student selected is a junior, given that the primary motivation is money is
(simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, if $n(A\cap B)$ is the number of elements in the intersection of $A$ and $B$, and $n(B)$ is the number of elements in $B$, then $P(A|B)=\frac{n(A\cap B)}{n(B)}$. Here, event $A$ is the student being a junior, and event $B$ is the student's primary motivation being money.

Step2: Identify $n(A\cap B)$ and $n(B)$

From the table, the number of juniors whose primary motivation is money $n(A\cap B) = 9$. The total number of students whose primary motivation is money $n(B)=31$.

Step3: Calculate the probability

$P(A|B)=\frac{n(A\cap B)}{n(B)}=\frac{9}{31}$

Answer:

$\frac{9}{31}$