Start with calculating the relative frequency. Try to identify the values that the student used to obtain their result and analyze the error.
See solution.
Practice makes perfect
A student calculated the relative frequency of those who do not support the issue given that they are Republican. Their result was 3333+36≈ 0.478. We want to identify the error they have made. Consider the given table.
Supports the Issue
Does Not Support the Issue
Totals
Democrat
24
36
60
Republican
27
33
60
Totals
51
69
120
To calculate the relative frequency we need to divide the number of Republicans who do not support the issue, 33, by the total number of asked people, 120.
Relative Frequency=33/120=0.275
The obtained result is different from the one calculated by the student. Let's try to identify the values the student used.
Student's Result:33/33+ 36
As we previously identified, 33 is the number of Republicans who do not support the issue, so the value in the numerator is correct. In the denominator there is a sum of the number of Republicans and Democrats who do not support the issue. Therefore, it is the total number of people not supporting the issue.
Republicans Not Supporting/Total Not Supporting=33/33+36
Therefore, the student calculated the conditional probability that a Republican is chosen, given that they do not support the issue. To find the correct relative frequency, they should have used the total number of people in the denominator.
