Question

1. the two - way frequency table shows how juniors and seniors get to school each day. mode of transportation

grade

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

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

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of 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 $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of students who are juniors and drive, and $n(B)$ is the number of students who drive.

Step2: Identify values from the table

From the table, the number of students who drive ($n(B)$) is 96, and the number of students who are juniors and drive ($n(A\cap B)$) is 42.

Step3: Calculate the probability

$P(\text{junior}|\text{drive})=\frac{42}{96}=\frac{7}{16}=0.4375 = 43.75\%\approx43.8\%$

Answer:

43.8%