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The method 100 students use to get to school and their grade level is shown below.

\begin{tabular}{|c|c|c|c|c|}
\hline & Drive & Bus & Walk & Total \\
\hline Sophomore & 2 & 25 & 3 & 30 \\
\hline Junior & 13 & 20 & 2 & 35 \\
\hline Senior & 25 & 5 & 5 & 35 \\
\hline Total & 40 & 50 & 10 & 100 \\
\hline
\end{tabular}

Find the probability that a student takes the bus, given that they are a junior.

[tex]\[ P(\text{bus} \mid \text{junior}) = \frac{P(\text{bus and junior})}{P(\text{junior})} = \frac{20}{35} \approx [?] \][/tex]

Round to the nearest hundredth.



Answer :

GinnyAnswer
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].

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