7. the two - way frequency table shows how juniors and seniors get to school each day. mode of…
7. the two - way frequency table shows how juniors and seniors get to school each day. mode of transportation\ngrade\n| |senior|junior|total|\n|--|--|--|--|\n|drive|54|42|96|\n|bus|19|22|41|\n|walk|11|7|18|\n|other|15|12|27|\n|total|99|83|182|\nwhat is the probability that a student is a junior given that they drive to school?\nclear all\n86.5%\n50.6%\n43.8%\n23.1%
Answer
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%