Let's complete the two-way table and calculate the probability step-by-step.
### Step 1: Calculate the total number of male students
We know that there are 28 males who participated in cycling and 19 males who participated in swimming.
Total number of male students:
[tex]\[ 28 + 19 = 47 \][/tex]
So the value in the table for the total number of males is:
[tex]\[ 47 \][/tex]
### Step 2: Calculate the number of female students who participated in swimming
We know there are 43 female students in total and 32 of them participated in cycling.
Number of female students who participated in swimming:
[tex]\[ 43 - 32 = 11 \][/tex]
So the value in the table for females who participated in swimming is:
[tex]\[ 11 \][/tex]
### Step 3: Calculate the number of students who participated in swimming
Total number of students who participated in swimming is the sum of males who swim and females who swim.
Total number of students who participated in swimming:
[tex]\[ 19 + 11 = 30 \][/tex]
### Step 4: Complete the table
Now, let's fill in the calculated values into the two-way table:
\begin{tabular}{|c|c|c|c|}
\hline & Cycling & Swimming & Total \\
\hline Males & 28 & 19 & 47 \\
\hline Females & 32 & 11 & 43 \\
\hline Total & & 30 & 90 \\
\hline
\end{tabular}
### Step 5: Calculate the probability that a randomly chosen student participated in swimming
Total number of students who participated in swimming is 30.
Probability that a randomly chosen student participated in swimming:
[tex]\[
\frac{\text{Number of students who participated in swimming}}{\text{Total number of students}} = \frac{30}{90} = \frac{1}{3}
\][/tex]
### Summary
1. Complete the table entries
2. Calculate the probability as [tex]$\frac{1}{3}$[/tex]
Let's fill these answers into the boxes:
1. The total number of male students is:
[tex]\[ 47 \][/tex]
2. The number of female students who participated in swimming is:
[tex]\[ 11 \][/tex]
3. The probability that a randomly chosen student participated in swimming is:
[tex]\[ \frac{1}{3} \][/tex]
