Consider a game with three times t0<t1<t2 . A pair of fair dice, one red and one blue are rolled at time t0 but you do not see the result. At time t1 , you are told the number on the red die. Draw a state tree with path probabilities.
Consider a game with three times t0<t1<t2 . A pair of fair dice, one red and...
Conditional Expectation A player plays a game. A pair of fair dice is rolled, the outcome of the Red die is denoted by R and the outcome of the Yellow die is deonted by Y. The player does not get to see the outcome of each die but is told the total sum of the two dice, denoted S. She wins W = $10 if the two dice have the same value (like Y = 4, R = 4 or...
Question 6 3 pts Exercise f. Consider the experiment in which three fair (and independent) dice are rolled: a red 4-sided die, a white 6-sided die and a blue 8-sided die. What is the probability that the highest rollis exactly 4? Question 7 3 pts Exercise g. Consider the experiment in which three fair (and independent) dice are rolled: a red 4-sided die, a white 6-sided die and a blue 8-sided die. What is the probability that the 4-sided die...
The following dice game is offered to you. You may simultaneously roll one red die and three blue dice. The stake is $1. If none of the blue dice matches the red die, you lose your stake; otherwise, you get anyway paid k + 1 dollars if exactly k of the blue dice match the red die. In the case that exactly one blue die matches the red die, you get paid an additional $0.50 if the other two blue...
A friend bets you $100 on a game involving two six-sided dice, one red and one green. You choose the number of times the pair of dice will be rolled. You win if the number of times a red 6 is rolled is at most 2 and the number of times a green 6 is rolled is at least 2. a) How many times should the dice be rolled to maximise your chance of winning? b) With that number of...
You roll a pair of fair 6-sided dice: a red die and a blue die. (a) Consider event A: {the outcome of the red die is more than 3} and event B: {the outcome of the red die is less than 5}. Given that event A occurs, what is the probability that event B occurs? (b) Are A and B mutually exclusive (i.e., disjoint)? (c) Are A and B independent? (d) Calculate the probability of event C: {the outcome of...
You roll a pair of fair 6-sided dice: a red die and a blue die. (a) Consider event A: {the outcome of the red die is more than 3} and event B: {the outcome of the red die is less than 5}. Given that event A occurs, what is the probability that event B occurs? (b) Are A and B mutually exclusive (i.e., disjoint)? (c) Are A and B independent? (d) Calculate the probability of event C: {the outcome of...
In a dice game, you roll a fair die three times, independently. If you don’t roll any sixes, you lose 1 dollar. If you roll a six exactly once, you win one dollar. If you roll a six exactly twice, you win two dollars. If you roll a six all three times, you win k dollars. (A) Let k = 3. What is the expected value of the amount you would win by playing this game (rounded to the nearest...
Two fair dice, one blue and one red, are tossed, and the up face on each die is recorded. Define the following events: E:{The sum of the numbers is even } F:{A6 on the blue die } Find the following probabilities:(a) P(E)=18 / 36(b) P(F)=4 / 36(c) P(E ∩ F)=Are events E and F independent?A. yesB. no
The game Monopoly is played with a pair of fair, distinguishable dice. Every time you roll doubles (both dice show the same number) you get to roll again immediately. However, if you roll doubles three times in a row on the same turn you are sent directly to Jail. What is the probability of being sent to jail in this manner? (Note: Each roll of the dice is independent of all other rolls.) (Express your answer as a fraction in...
1) You roll 2 fair dice, a green one and a red one. a. What is P(a 1 on green die and a three on red die)? b. What is P((one on green die and three on red die) or (three on green die and one on red die))? c. What is the probability of getting a sum of 11?