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Below, a two-way table is given for student activities:

\begin{tabular}{|c|c|c|c|c|}
\hline
& Sports & Drama & Work & Total \\
\hline
Sophomore & 20 & 7 & 3 & 30 \\
\hline
Junior & 20 & 13 & 2 & 35 \\
\hline
Senior & 25 & 5 & 5 & 35 \\
\hline
Total & 65 & 25 & 10 & 100 \\
\hline
\end{tabular}

Follow the steps to find the probability a student is in sports, given that they are a senior.

First, find the probability that a student is a senior:
[tex]\[
P \text { (senior) } = \frac{35}{100} = 0.35
\][/tex]

Next, find the probability that a student is in sports given that they are a senior:
[tex]\[
P \text { (sports | senior) } = \frac{25}{35}
\][/tex]

Enter your answer in decimal form. Do not round.
[tex]\[ \boxed{\ } \][/tex]



Answer :

GinnyAnswer
To find the probability that a student is a senior, we need to follow these steps:

1. Identify the total number of students.
According to the provided table, the total number of students is 100.

2. Identify the number of senior students.
From the table, the number of senior students is 35.

3. Calculate the probability.
The probability that a student is a senior is calculated by dividing the number of senior students by the total number of students. This is done as follows:

[tex]\[ P(\text{Senior}) = \frac{\text{Number of senior students}}{\text{Total number of students}} \][/tex]

[tex]\[ P(\text{Senior}) = \frac{35}{100} \][/tex]

[tex]\[ P(\text{Senior}) = 0.35 \][/tex]

So, the probability that a student is a senior is [tex]\(0.35\)[/tex].

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