To find the probability that a student takes the bus, given that they are a junior, we need to use the concept of conditional probability. The formula for conditional probability is:
[tex]\[ P(\text{bus} \mid \text{junior}) = \frac{P(\text{bus and junior})}{P(\text{junior})} \][/tex]
Let's break this down step-by-step:
1. Identify the total number of juniors:
According to the provided table, there are 35 juniors in total.
2. Identify the number of juniors who take the bus:
The table shows that 20 juniors take the bus.
Now, let's apply the conditional probability formula using these values:
[tex]\[ P(\text{bus} \mid \text{junior}) = \frac{\text{Number of juniors who take the bus}}{\text{Total number of juniors}} \][/tex]
Substitute the values we identified:
[tex]\[ P(\text{bus} \mid \text{junior}) = \frac{20}{35} \][/tex]
3. Simplify and round the result:
When you perform the division and round to the nearest hundredth, you get:
[tex]\[ P(\text{bus} \mid \text{junior}) = 0.57 \][/tex]
Thus, the probability that a student takes the bus, given that they are a junior, is approximately [tex]\(0.57\)[/tex].
