Suppose that you roll 2 dice and consider the sum of the two. Let A be the event of throwing odd, B be the event of throwing 4 or less and C be the event of throwing a multiple of 3.
a) What is the sample space S and the corresponding probability of each element of S.
b) Compute P(A), P(B) and P(C). Which rule do you see?
c) Which elements belong to AUB?
d) Show that P(AUB) is 11/18.
e) Which elements belong to AnB? find out P(AnB).
f) find out P(A|B) by rule F, and then show with Rule E that A and B are not independent.
g) Which elements belong to AnC? show that P(AnC) is 1/6.
h) find out P(A|C) by rule F and then show with Rule E that A and C are independent.