3.Rolling two dice.

Let X1: faced value of the 1st die; X2: faced value of the 2nd die; Y: the sum of two dice.Find:

a.P (X1 = 3 X2 = 6)

b.P (X1 = 5 X2 = 1)

c.P(X2 2 | X1 > 4)

d.P (X1 = 4 | Y 8)

4.Flip a fair coin twice.

Let H: the coin lands on a head;T: the coin lands on a tail. S = {(H, H), (H, T), (T, H), (T, T)}

Find:

a.P (both are H)

b.P (1st is T 2nd is H)

c.P (both are T | at least one T)

d.P (2nd is H | both are T)

e.P (at least one H | 2nd is T)

5.Randomly select one card from a well shuffled deck of cards. Let A: the select card is an ace; D: the select card is a diamond. Find:

a.P (A)

b.P (D)

c.P (A D)

d.P (A D)

e.P (A | D)

f.P (D | A)

Two cards are being randomly selected without replacement.

g.What's the probability that both cards are ace?

h.What's the probability that the first card is a red king and the second card is a black

king?