# Question: A board game requires players to roll a pair of

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.

a. List the sample space of the 36 possible outcomes for the two dice.

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.

c. Let B be the event that the sum on the pair of dice is 7. Find P(B).

d. Find the probability of (i) A and B, (ii) A or B, and (iii) B given A.

e. Are events A and B independent, disjoint, or neither? Explain.

a. List the sample space of the 36 possible outcomes for the two dice.

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.

c. Let B be the event that the sum on the pair of dice is 7. Find P(B).

d. Find the probability of (i) A and B, (ii) A or B, and (iii) B given A.

e. Are events A and B independent, disjoint, or neither? Explain.

## Answer to relevant Questions

Refer to the previous exercise. Define event D as rolling an odd sum with two dice. 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) = ...For the decision about whether to convict someone charged with murder and give the death penalty, consider the variables reality (defendant innocent, defendant guilty) and decision (convict, acquit). a. Explain what the two ...A fast food chain is running a promotion to try to increase sales. Each customer who purchases a meal combo receives a game piece that contains one of the letters U, W, I, or N. If a player collects one of all four letters, ...From past experience, a wheat farmer living in Manitoba, Canada finds that his annual profit (in Canadian dollars) is $80,000 if the summer weather is typical, $50,000 if the weather is unusually dry, and $20,000 if there is ...For a normal distribution, a. Show that a total probability of 0.01 falls more than z = 2.58 standard deviations from the mean. b. Find the z -score for which the two-tail probability that falls more than that many standard ...Post your question