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?

Here's how to solve this probability problem: Step 1: Identify the given information. 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 B) = 20 Step 2: Define the events and their probabilities. 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 B). The probability of choosing a woman is: P(W) = (N_W)/(Total seniors) = (98)/(200) The probability of choosing a Biology major is: P(B) = (N_B)/(Total seniors) = (34)/(200) The probability of choosing a Biology major who is also a woman (the intersection) is: P(W B) = N_W BTotal seniors = (20)/(200) Step 3: Use the formula for the probability of the union of two events. The formula is P(W B) = P(W) + P(B) - P(W B). Substitute the probabilities: P(W B) = (98)/(200) + (34)/(200) - (20)/(200) Step 4: Calculate the sum and simplify the fraction. P(W B) = (98 + 34 - 20)/(200) P(W B) = (132 - 20)/(200) P(W B) = (112)/(200) To simplify, divide both the numerator and the denominator by their greatest common divisor. Both are divisible by 8: P(W B) = (112 ÷ 8)/(200 ÷ 8) = (14)/(25) The probability is (14)/(25). That's 2 down. 3 left today — send the next one.