Chapter 5, Problem 80CP

Roll two more dice Refer to the previous exercise. Define event D as rolling an odd sum with two dice.

1. a. B denotes a sum of 7 on the two dice. Find P(B and D). When an event B is contained within an event D, as here, explain why P(B and D) = P(B).
2. b. Find P(B or D). When an event B is contained within an event D, explain why P(B or D) = P(D).

5.79 Board games and dice A board game requires players to roll a pair of balanced dice for each player’s turn. Denote the outcomes by (die 1, die 2), such as (5, 3) for a 5 on die 1 and a 3 on die 2.

1. a. List the sample space of the 36 possible outcomes for the two dice.
2. b. Let A be the event that you roll doubles (that is, each die has the same outcome). List the outcomes in A and find its probability.
3. c. Let B be the event that the sum on the pair of dice is 7. Find P(B).
4. d. Find the probability of (i) A and B, (ii) A or B, and (iii) B given A.
5. e. Are events A and B independent, disjoint, or neither? Explain.