In a university, 30% of the students major in Business management, 25% major in mathematics and 10% major in both business management and mathematics. A student from this university is selected at random.

Question

A) what is the probability that the student majors in business management or mathematics?
B) what is the probability that the student majors in neither of these two courses?

Answer 1

A = Business management
B = mathematics

a)
P(A U B) = P(A) + P(B) - P(A ∩ B)
= 0.3 + 0.25 - 0.1
= 0.45

b)
P(not A and not B)
= P(A' ∩ B')
= 1 - P(A U B)
= 1 - 0.45
= 0.55

Answer 2

Suppose that a drug is known to be 90% effective in treating a certain disease. What is the probability that it will be successful in treating seven to ten out of 12 patients with the disease?