Suppose that 70% of the seniors at a large university have taken calculus, and 30% of the seniors have taken physics. Of the seniors who have taken calculus, 40% have taken physics. A student who is a senior at this university is randomly selected. Define the following events.
A = The student has taken calculus
B = The student has taken physics
-Which of the following is true about the events A and B?
A) A and B are mutually exclusive.
B) A and B are complements.
C) A and B are independent.
D) None of the above.

Question

Quizplus · Accepted Answer

The events A and B are not mutually exclusive because some students have taken both calculus and physics. They are not complements because a student can take both or neither. They are not independent because the probability of taking physics given that a student has taken calculus is different from the overall probability of taking physics.

Suppose That 70% of the Seniors at a Large University