Question

Look at the two-way frequency table below.

Freshman Sophomore Junior Senior Total
Male 208 148 186 360 902
Female 320 132 214 280 946
Total 528 280 400 640 1,848
What is the best approximation of the probability a student is male, given the student is a freshman?

A.
10%

B.
25%

C.
40%

D.
60%

Answer 1

To find the probability that a student is male given that the student is a freshman, we can use the formula for conditional probability:

\[
P(\text{Male} | \text{Freshman}) = \frac{P(\text{Male} \cap \text{Freshman})}{P(\text{Freshman})}
\]

In this context, we can find the number of male freshmen and the total number of freshmen from the table:

- The number of male freshmen is 208.
- The total number of freshmen is 528.

So, we calculate the probability:

\[
P(\text{Male} | \text{Freshman}) = \frac{208}{528}
\]

Calculating the above fraction:

\[
P(\text{Male} | \text{Freshman}) = \frac{208}{528} \approx 0.394
\]

To express this as a percentage, multiply by 100:

\[
0.394 \times 100 \approx 39.4\%
\]

Rounding this to the nearest option available, the best approximation of the probability is approximately 40%.

Thus, the correct answer is:

**C. 40%**