show how events are not independent

Question

A is the event that Ny Giants football team will qualify for the championship. B is the event that they will win against Minnesota. If (A)=52% , P(B)=79% , AND P(A and B) is 4% .

a.show how the events are not independent

b.Ac

c.AnB

d.AUB

c.Ac U B

f.Ac n Bc

Answer 1

 

Let P(A) be the probability of A, P(B) - probability of B. Then the probability for (AUB) is defined by

P(AUB) =P(A) + P(B) - P(A∩B) = 0.52 + 0.79 - 0.04 = 1.27.

The probability should be less than 1. If the calculated probability exceeds 1 that means the probability for the event B is dependent on probability of the event A to occur. For two independent events we must have

      P(A∩B) = P(A)P(B) = 0.52 x 0.79 = 0.395, almost ten times more what it actually is (= 4%).

I can't understand other notations (such as Ac, Bc??).