SOLUTION: Consider the experiment of rolling two dice (one die is blue and the other is red) and the following events: A: ‘The sum of the dice is 8’ and B: ‘Both dice have even numbe

Algebra ->  Test -> SOLUTION: Consider the experiment of rolling two dice (one die is blue and the other is red) and the following events: A: ‘The sum of the dice is 8’ and B: ‘Both dice have even numbe      Log On


   

Question 1028444: Consider the experiment of rolling two dice (one die is blue and the other is red) and the following events:
A: ‘The sum of the dice is 8’ and B: ‘Both dice have even numbers’ and C: “The difference (absolute value) of the dice is 2” and D: “the blue die has an even number”
Find (a) p(A and B) (HINT: You cannot assume these are independent events.)
(b) p(A or B)
(c) Are A and B mutually exclusive events? To Explain.
(d) Are A and B independent events? Explain. (no explanations no points)
(e) Are C and D independent events? Explain. (no explanations no points)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
(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%2F36+%2B+1%2F4+-+1%2F12+=+11%2F36
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%28A+and+B%29%3C%3EP%28A%29P%28B%29.
(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%2F9+=+P%28C+and+D%29+=+P%28C%29P%28D%29+=+%282%2F9%29%281%2F2%29++=1%2F9