Question

Two six-sided fair dice are rolled simultaneously. The probability that the sum of the two numbers rolled is greater than 3, given that the sum of the numbers is not greater than 5, is . The probability that one of the numbers is a 6 and the sum of the two numbers is an odd number is .

Answer 1

A) Possible outcomes are ...
  (1, 3), (1, 4), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)
for a total of 7 out of 36 outcomes that match your requirements.
  p(3 < sum ≤ 5) = 7/36

B) Possible outcomes are ...
  (6, 1), (6, 3), (6, 5), (1, 6), (3, 6), (5, 6)
for a total of 6 out of 36 outcomes that match your requirements.
  p(6 and odd) = 6/36 = 1/6