Discuss the following:
Q1: Two fair dice are tossed, and the face on each die is observed.
a. Use a tree diagram to find the 36 sample points contained in the same space.
b. Assign probabilities to the sample points in part a.
c. Find the probability of each of the following events:
A = {3 showing on each die}
B = {sum of two numbers showing is 7}
C = {sum of two numbers showing is even}
Q2: A pair of fair dice is tossed. Define the following events:
A: {You will roll a 7} (i.e., the sum of the dots on the up faces of the two dice is equal to 7)
B: {At least one of the two dice shows a 4}
a. Identify the sample points in the events A, B, A upside down U B, A U B, and A^c.
b. Find P(A), P(B), P(A upside down U B), P(A U B), and P(A^c) by summing the probabilities of the appropriate sample points.
c. Find P(A U B) using the additive rule. Compare your answer to that for the same event in part b.
d. Are A and B mutually exclusive? Why?