Revised GRE Math Probability section The table shows the distribution of a group of $40$ college students by gender and class
$$
\begin{array}{c|lcr}
 &amp; \text{Sophomores} &amp; \text{Juniors} &amp; \text{Seniors} \\
\hline
\text{Males} &amp; 6 &amp; 10 &amp; 2 \\
\text{Females} &amp; 10 &amp; 9 &amp; 3 \\
\end{array}
$$

If one student is randomly selected from this group, find the probability that the student chosen is (i) a female or a sophomore?
How many students are either females or sophomores (or both)? First count the  number of females, then count the number of male sophomores (female sophomores need not be counted since you already counted them when you counted the number of females). What percent of the total number of students is this?

There are $10 + 9 + 3 = 22$ females and $6$ male sophomores, so there are $22 + 6 = 28$ students out of $40$ who are either female or sophomore.

$28/40 = 0.7$
The number of sophomores= 16


Number of females=10+9+3=22
Number of female sophomores=6

We get a venn diagram between sophomores and females, with common area as 6
Total people who are sophomore or female= 10+6+16=32

Probability=32/40=0.8