You have a six-sided die that you roll once. Let Ri denote the event that the roll is i. Let G j denote the event that the roll is greater than j. Let E denote the event that the roll of the die is even-numbered.
(a) What is P[R3|G1], the conditional probability that 3 is rolled given that the roll is greater than 1?
(b) What is the conditional probability that 6 is rolled given that the roll is greater than 3?
(c) What is P[G3|E], the conditional probability that the roll is greater than 3 given that the roll is even? (d) Given that the roll is greater than 3, what is the conditional probability that the roll is even?