In a class of 200 seniors, 98 are women, 34 are Biology majors, and 20 are women who are Biology majors. What is the probability that a randomly chosen senior is either a Biology major or a woman?

Total number of seniors = 200
Number of women ($N_W$) = 98
Number of Biology majors ($N_B$) = 34
Number of Biology majors who are women ($N_{W \cap B}$) = 20

Let $W$ be the event that a chosen student is a woman.
Let $B$ be the event that a chosen student is a Biology major.
We want to find the probability that the choice will be either a Biology major or a woman, which is $P(W \cup B)$.

The probability of choosing a woman is:

The probability of choosing a Biology major is:

The probability of choosing a Biology major who is also a woman (the intersection) is:

The formula is $P(W \cup B) = P(W) + P(B) - P(W \cap B)$.
Substitute the probabilities:

To simplify, divide both the numerator and the denominator by their greatest common divisor. Both are divisible by 8:

The probability is $\frac{14}{25}$.