A student calculated the relative frequency of those who do not support the issue given that they are Republican. Their result was $\frac{3 3}{3 3 + 3 6} \approx 0.478 .$ 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 = \frac{3 3}{1 2 0} = 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 : \frac{3 3}{3 3 + 3 6}

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.

\frac{Republicans Not Supporting}{Total Not Supporting} = \frac{3 3}{3 3 + 3 6}

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.

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