Answer :
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].
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].