We want to find the number of Sasha's teammates. We can start by calculating the sum of each row and column. Let's do it!
In English Class:& 4+2 = 6
Not in English Class:& 1+ 3 = 4
In Math Class:& 4+1 = 5
Not in Math Class:& 2+3 = 5
We can add this information to the table.
Math Class
Not in Math Class
Total
English Class
4
2
6
Not in English Class
1
3
4
Total
5
5
Finally, we have two ways of calculating the grand total. We can add the number of teammates who are in English class with Sasha to the number of teammates who are not in English class with her, or we can add the number of teammates who are in math class with Sasha to the number of teammates who are not in math class with her. These two numbers must be the same!
Grand Total
l 6+ 4 = 10 5+ 5= 10 âś“
Now we can complete our table!
Math Class
Not in Math Class
Total
English Class
4
2
6
Not in English Class
1
3
4
Total
5
5
10
Looking at the table, we can see that Sasha has 10 teammates.
We want to find the relative frequency of the number of Sasha's teammates that are in both of her classes to the number of all of her teammates. Let's look at the table from part A!
Math Class
Not in Math Class
Total
English Class
4
2
6
Not in English Class
1
3
4
Total
5
5
10
We can see in the table that out of 10 teammates, there are 4 teammates that attend both classes with Sasha. To find the missing frequency, we will now calculate the ratio of the number of Sasha's teammates that are in both of her classes to the number of all of her teammates.
4/10 = 0.4
The relative frequency of Sasha's teammates that are in both of her classes to the number of all of her teammates is equal to 0.4.
We want to find which percentage out of Sasha's teammates in her math class is greater, the percentage of teammates who are also in her English class or the percentage of teammates who are not in her English class. Let's look at the table from part A!
Math Class
Not in Math Class
Total
English Class
4
2
6
Not in English Class
1
3
4
Total
5
5
10
To find which percentage is greater, we will first identify the number of Sasha's teammates who are in her both her math and English classes, the number of Sasha's teammates who are in her math class but not in her English class, and the total number of students in her math class in the table.
Math Class
Not in Math Class
Total
English Class
4
2
6
Not in English Class
1
3
4
Total
5
5
10
We can see in the table that there are 5 teammates who attend the math class with Sasha. Out of those 5 teammates, 4 of them are in her English class and 1 is not. To compare the percentages, we can calculate the ratios of each value to the total number of teammates in Sasha's math class.
Math Class
Not in Math Class
Total
English Class
4; 4/5=0.80
2
6
Not in English Class
1; 1/5=0.20
3
4
Total
5; 5/5=1.00
5
10
We can use the calculated relative frequencies to compare the percentages.
Out of 5 teammates who are in Sasha's math class, 80 % of them are also in her English class.
Out of 5 teammates who are in Sasha's math class, 20 % of them are not in her English class.
We know that 80 % is greater than 20 %. This means that out of the teammates who are in Sasha's math class, the percentage of students who are also in her English class is greater.
