The probability that a college freshman takes a math class the first semester is 0.75. The probability that a college freshman takes an English class the first semester is 0.70. The
probability that a college freshman takes both a math class and an English class the first
semester is 0.60. Find the probability that a college freshman takes a math class or an English
class the first semester.

0.85

Explanation:

Using the addition law of probability which states that for two events A and B, the probability that A or B will occur is the sum of their individual probabilities minus the probability that both  A  and  B  will occur. The addition rule is given by the formula:

P(A or B) = P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Let probability that a college freshman takes a math class the first semester = P(A) = 0.75

probability that a college freshman takes an English class the first semester = P(B) = 0.70

probability that a college freshman takes both a math class and an English class the first  semester = P(A ∩ B) = 0.60

the probability that a college freshman takes a math class or an English  class the first semester = P(A ∪ B) = P(A or B)

Therefore, P(A or B) = P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.75 + 0.7 - 0.6 = 0.85

P(A or B) = 0.85