Answer :
To solve the problem of finding the probability that a student takes the bus given that they are a junior, we can use the following steps:
1. Identify the total number of juniors.
- From the table, we see that there are 35 juniors in total.
2. Identify the number of juniors who take the bus.
- From the table, we find that there are 20 juniors who take the bus.
3. Calculate the probability of taking the bus given that the student is a junior.
- The formula for conditional probability is:
[tex]\[ P(\text{bus} \mid \text{junior}) = \frac{P(\text{bus and junior})}{P(\text{junior})} \][/tex]
- Here, \(P(\text{bus and junior})\) refers to the probability that a student is both a junior and takes the bus, which can be given as the ratio of juniors who take the bus to the total number of students. However, since we are only focusing on juniors, we simplify to count the number of juniors who take the bus over the total number of juniors.
- Therefore, the conditional probability simplifies to:
[tex]\[ P(\text{bus} \mid \text{junior}) = \frac{\text{Number of juniors who take the bus}}{\text{Total number of juniors}} = \frac{20}{35} \][/tex]
4. Simplify the fraction and round to the nearest hundredth.
- The raw calculation gives us:
[tex]\[ \frac{20}{35} \approx 0.57142857 \][/tex]
- When rounded to the nearest hundredth, this results in:
[tex]\[ 0.57 \][/tex]
Therefore, the probability that a student takes the bus given that they are a junior is:
[tex]\[ \boxed{0.57} \][/tex]
1. Identify the total number of juniors.
- From the table, we see that there are 35 juniors in total.
2. Identify the number of juniors who take the bus.
- From the table, we find that there are 20 juniors who take the bus.
3. Calculate the probability of taking the bus given that the student is a junior.
- The formula for conditional probability is:
[tex]\[ P(\text{bus} \mid \text{junior}) = \frac{P(\text{bus and junior})}{P(\text{junior})} \][/tex]
- Here, \(P(\text{bus and junior})\) refers to the probability that a student is both a junior and takes the bus, which can be given as the ratio of juniors who take the bus to the total number of students. However, since we are only focusing on juniors, we simplify to count the number of juniors who take the bus over the total number of juniors.
- Therefore, the conditional probability simplifies to:
[tex]\[ P(\text{bus} \mid \text{junior}) = \frac{\text{Number of juniors who take the bus}}{\text{Total number of juniors}} = \frac{20}{35} \][/tex]
4. Simplify the fraction and round to the nearest hundredth.
- The raw calculation gives us:
[tex]\[ \frac{20}{35} \approx 0.57142857 \][/tex]
- When rounded to the nearest hundredth, this results in:
[tex]\[ 0.57 \][/tex]
Therefore, the probability that a student takes the bus given that they are a junior is:
[tex]\[ \boxed{0.57} \][/tex]
