Question

the frequency table shows how juniors and seniors get to school each day.

	junior	senior	total
bus	22	19	41
walk	7	11	18
other	12	15	27
total	83	99	182

what is the probability that a student is a junior given that they drive to school
23.1% 43.8% 50.6% 86.5%

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 frequencies in a two - way table, if $A$ is the event that a student is a junior and $B$ is the event that a student drives to school, then $P(A|B)=\frac{\text{Number of juniors who drive}}{\text{Total number of students who drive}}$.

Step2: Identify relevant values from the table

The number of juniors who drive is 42, and the total number of students who drive is $42 + 54=96$.

Step3: Calculate the probability

$P(\text{junior}|\text{drive})=\frac{42}{96}=\frac{7}{16}=0.4375 = 43.75\%$

Answer:

43.75%