The following probabilities are known: P(A) = 0.2, P(B) = 0.25, and P(C) = 0.3.
ID: 3205630 • Letter: T
Question
The following probabilities are known: P(A) = 0.2, P(B) = 0.25, and P(C) = 0.3. P(A B) = 0.05 and P(A c) = 0.6 Are events A and B independent? Show how you came to this conclusion. Are events A and C independent? Show how you came to this conclusion. An oil exploration company currently has two active projects, one in Alabama and the other in Texas. Let A be the event that the Alabama project is successful and T be the event that the Texas project is successful. Suppose that A and B are independent events with P(A) = 0.4 and P(B) 0.7. If the Alabama project is not successful, what is the probability that the Texas project is also not successful? b) What is the probability that at least one of the two projects will be successful?Explanation / Answer
a)for P(A)*P(B) =0.2*0.25=0.05 which is equal to P(AnB) . Hence they are independent.
b)P(A).P(C) =0.2*0.3=0.06 which is not equal to P(AnC). Hence not independent
5)here P(A) =0.4
and P(B)=0.7
as both the projects are independent, hence texas project success or failure is independent of Alabama project
a)therefore probabilty of Texas project failure=1-0.7 =0.3
b) for at least one project to be successful P(AuB) =P(A)+P(B)-P(A)P(B) =0.4+0.7-0.4*0.7 =0.82
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.