the method 100 students use to get to school and their grade level is shown below.\n| |drive|bus|walk|total|\…

the method 100 students use to get to school and their grade level is shown below.\n| |drive|bus|walk|total|\n|--|--|--|--|--|\n|sophomore|2|25|3|30|\n|junior|13|20|2|35|\n|senior|25|5|5|35|\n|total|40|50|10|100|\nfind the probability a student takes the bus, given that they are a sophomore.\np(bus | sophomore) = \\frac{p(bus and sophomore)}{p(sophomore)} = ?\nround to the nearest hundredth

the method 100 students use to get to school and their grade level is shown below.\n| |drive|bus|walk|total|\n|--|--|--|--|--|\n|sophomore|2|25|3|30|\n|junior|13|20|2|35|\n|senior|25|5|5|35|\n|total|40|50|10|100|\nfind the probability a student takes the bus, given that they are a sophomore.\np(bus | sophomore) = \\frac{p(bus and sophomore)}{p(sophomore)} = ?\nround to the nearest hundredth

Answer

Explanation:

Step1: Identify relevant values

The number of sophomores who take the bus is 25, and the total number of sophomores is 30.

Step2: Calculate the conditional - probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of the table values, $P(\text{bus}|\text{sophomore})=\frac{\text{Number of sophomores who take the bus}}{\text{Total number of sophomores}}$. So $P(\text{bus}|\text{sophomore})=\frac{25}{30}=\frac{5}{6}\approx0.83$.

Answer:

$0.83$