probability homework

Question

 the probability that an exam coverage will be about chapter 1 is 0.45, the probability that it will cover chapter 2 is 0.63 and the probability that it will cover either chapter 1 and 2 or both is 0.76. what is the probability that the coverage of the exam will come from:

 

both chapters?

neither chapters?

Answer 1

Let A = "exam covers chapter 1"

     B = "exam covers chapter 2"

 

You know that P(A) = 0.45; P(B) = 0.63, and P(A or B) = 0.76.

 

You are asked P(A and B) and there is a formula for it,right?

Recall that P(A or B) = P(A) + P(B) - P(A and B)....

Just a little algebra and you will get your P(A and B)........

 

If C="Exam does not cover chapter 1 or chapter 2", then C is the complement of the event (A or B), right? . In general,  if D' is the complement of D, we know that P(D') = 1- P(D), so in your case ..... 

 

You should be able to complete this simple problem on your own now.