Answer :
To address the question, let's break it down into two parts as per the table provided.
### Part (a): Number of Boys Who Can Count
First, we need to determine how many boys can count. According to the table:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & Boys & Girls & Total \\ \hline Can count & 42 & 58 & 100 \\ \hline Cannot count & 11 & 9 & 20 \\ \hline Total & 53 & 67 & 120 \\ \hline \end{tabular} \][/tex]
The number of boys who can count is listed directly in the table under the row labeled "Can count" in the column labeled "Boys".
So, the number of boys who can count is:
[tex]\[ 42 \][/tex]
### Part (b): Probability That Any Pupil is a Boy and Can Count
Next, we need to find the probability that any randomly selected pupil is a boy who can count.
Probability is defined as the ratio of favorable outcomes to the total number of possible outcomes. In this case:
- Favorable outcomes: The number of boys who can count, which is 42.
- Total outcomes: The total number of pupils, which is 120.
Thus, the probability [tex]\(P\)[/tex] can be calculated as:
[tex]\[ P(\text{boy and can count}) = \frac{\text{Number of boys who can count}}{\text{Total number of pupils}} = \frac{42}{120} \][/tex]
Now, we simplify:
[tex]\[ \frac{42}{120} = \frac{7}{20} = 0.35 \][/tex]
So, the probability that any randomly chosen pupil is a boy who can count is:
[tex]\[ 0.35 \][/tex]
### Summary
- Number of boys who can count: [tex]\(42\)[/tex]
- Probability that any pupil is a boy and can count: [tex]\(0.35\)[/tex]
These results provide the complete step-by-step solution to the question based on the information provided in the table.
### Part (a): Number of Boys Who Can Count
First, we need to determine how many boys can count. According to the table:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & Boys & Girls & Total \\ \hline Can count & 42 & 58 & 100 \\ \hline Cannot count & 11 & 9 & 20 \\ \hline Total & 53 & 67 & 120 \\ \hline \end{tabular} \][/tex]
The number of boys who can count is listed directly in the table under the row labeled "Can count" in the column labeled "Boys".
So, the number of boys who can count is:
[tex]\[ 42 \][/tex]
### Part (b): Probability That Any Pupil is a Boy and Can Count
Next, we need to find the probability that any randomly selected pupil is a boy who can count.
Probability is defined as the ratio of favorable outcomes to the total number of possible outcomes. In this case:
- Favorable outcomes: The number of boys who can count, which is 42.
- Total outcomes: The total number of pupils, which is 120.
Thus, the probability [tex]\(P\)[/tex] can be calculated as:
[tex]\[ P(\text{boy and can count}) = \frac{\text{Number of boys who can count}}{\text{Total number of pupils}} = \frac{42}{120} \][/tex]
Now, we simplify:
[tex]\[ \frac{42}{120} = \frac{7}{20} = 0.35 \][/tex]
So, the probability that any randomly chosen pupil is a boy who can count is:
[tex]\[ 0.35 \][/tex]
### Summary
- Number of boys who can count: [tex]\(42\)[/tex]
- Probability that any pupil is a boy and can count: [tex]\(0.35\)[/tex]
These results provide the complete step-by-step solution to the question based on the information provided in the table.
