math125 GMU

4. Assume a biased die has P(1) = 1, P(2) = ;, P(3) = P(4) = {, P(5) = 1, P(6) = 5. If die is tossed twice, find the probability that (a) the sum of the numbers appearing is 8. (b) the sum of the numbers is even. (c) the numbers that appear differ by 4. (d) the numbers that appear differ by at least 4. (e) let A be the "the sum of the numbers is even" and B be "the numbers that appear differ by at least 4", find P(A | B) and P(B | A). Are A and B independent