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 rides the bus, given that they are a senior.\np(bus | senior) = \\frac{p(bus and senior)}{p(senior)} = ?\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 rides the bus, given that they are a senior.\np(bus | senior) = \\frac{p(bus and senior)}{p(senior)} = ?\nround to the nearest hundredth.

Answer

Explanation:

Step1: Identify P(bus and senior)

The number of seniors who ride the bus is 5, and the total number of students is 100. So $P(\text{bus and senior})=\frac{5}{100}$.

Step2: Identify P(senior)

The number of seniors is 35, and the total number of students is 100. So $P(\text{senior})=\frac{35}{100}$.

Step3: Calculate P(bus|senior)

Using the formula $P(\text{bus}|\text{senior})=\frac{P(\text{bus and senior})}{P(\text{senior})}$, we substitute the values: $P(\text{bus}|\text{senior})=\frac{\frac{5}{100}}{\frac{35}{100}}=\frac{5}{35}\approx 0.14$.

Answer:

0.14