Statistics Question Joe is the charge of helping students wi

Statistics Question:

Joe is the charge of helping students with computer programs in the Math department. Let A denote the event that the next question for Joe is about MATLAB and let B denote the event the next question for Joe is about R. Suppose that P(A)=0.30 and P(B)=0.50. Why is it not the case that P(A)+P(B)=1? Calculate P(A^c). Calculate P(AUB). Calculate P(A^c B^c).

Solution

a)Since, the two events are independent thus P(A)+P(B) is not equal to one.

b)P(A union B)=P(A)+P(B)-P(A)*P(B)

=0.3+0.5-0.3*0.5

=0.65

b)P(AC)=1-0.3=0.7

d)P(Ac intersection B c)=0.7*0.5=0.35