Let's fill in the two-way table and answer the probability question step-by-step.
1. Determine the Total Number of Males:
Males who are cycling: 28
Males who are swimming: 19
Total number of males:
[tex]\[
28 + 19 = 47
\][/tex]
So, the total number of males is 47. We can fill this into the table as follows:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& Cycling & Swimming & Total \\
\hline
Males & 28 & 19 & 47 \\
\hline
Females & 32 & & 43 \\
\hline
Total & & & 90 \\
\hline
\end{tabular}
\][/tex]
2. Determine the Number of Females Swimming:
We know the total number of females is 43 and the number of females cycling is 32.
Therefore, the number of females swimming is:
[tex]\[
43 - 32 = 11
\][/tex]
Now update the table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& Cycling & Swimming & Total \\
\hline
Males & 28 & 19 & 47 \\
\hline
Females & 32 & 11 & 43 \\
\hline
Total & & & 90 \\
\hline
\end{tabular}
\][/tex]
3. Calculate the Total Number of Students Cycling and Swimming:
Total number of students cycling:
[tex]\[
28 + 32 = 60
\][/tex]
Total number of students swimming:
[tex]\[
19 + 11 = 30
\][/tex]
Now update the table fully:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& Cycling & Swimming & Total \\
\hline
Males & 28 & 19 & 47 \\
\hline
Females & 32 & 11 & 43 \\
\hline
Total & 60 & 30 & 90 \\
\hline
\end{tabular}
\][/tex]
4. Probability Calculation:
The probability that a randomly chosen student participated in swimming is given by the ratio of the number of students swimming to the total number of students.
Number of students swimming: 30
Total number of students: 90
Thus, the probability is:
[tex]\[
\frac{30}{90} = \frac{1}{3}
\][/tex]
So, the probability that a randomly chosen student participated in swimming is [tex]\(\frac{1}{3}\)[/tex].
