A student is taking two courses history and math The probabi

A student is taking two courses, history and math. The probability the student will pass the history course is 0.75, and the probability of passing the math course is 0.65. The probability of passing both is 0.5. What is the probability of passing at least one? Please show work.

Solution

Let

H = history
M = math

P(pass at least one) = P(H or M)

As

P(H or M) = P(H) + P(M) - P(H and M)

Then

P(H or M) = 0.75 + 0.65 - 0.5 = 0.90 [ANSWER]