One Advanced Maths Initial Assessment

Question 14

90 students went on an activity day.
Complete the two-way table below.

\begin{tabular}{|c|c|c|c|}
\hline & Cycling & Swimming & Total \\
\hline Males & 28 & 19 & [tex]$\square$[/tex] \\
\hline Females & 32 & [tex]$\square$[/tex] & 43 \\
\hline Total & [tex]$\square$[/tex] & [tex]$\square$[/tex] & 90 \\
\hline
\end{tabular}

One of these students is chosen at random.
What is the probability that this student participated in swimming?
Give your answer as a fraction in its simplest form.



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].