Question 1028444
(a) P(A & B) = 3/36  = 1/12
Of the five pairs that will give a sum of 8, only three are both even.

(b)  P(A or B) = P(A) + P(B) - P(A&B) = {{{5/36 + 1/4 - 1/12 = 11/36}}}
by the addition law of probability.

(c)  Are A and B mutually exclusive events? NO, because P(A & B) is NOT equal to zero.

(d)  Are A and B independent events? NO, because P(A) = 5/36, P(B) = 1/4, P(A&B) = 1/12, and so {{{P(A and B)<>P(A)P(B)}}}.

(e)  Are C and D independent events? YES.  P(C & D) = 4/36 = 1/9.
Now P(C) = 8/36 = 2/9, while P(D) = 1/2.

==> {{{1/9 = P(C and D) = P(C)P(D) = (2/9)(1/2)  =1/9}}}