Suppose you roll a pair of fair dice 10 times. What's the probability that you'll roll...
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...
A pair of fair dice is tossed 6 times. Find probability that : 1) a total of 7 is obtained 3 times 3) a matching pair occurs 3 times 2) a totall of 7 and 11 is obtained 4 times 4) a total of 11 and matching pair occurs twice how to find these using excel
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...
Suppose you roll two fair 10-sided dice. Each dice has its faces labeled 1 through 10 and by "fair" we mean each face is equally likely to appear. What is the probability that both dice show the same face? Note: Give an exact answer as a fraction in the form a/b (explained) Number A fair coin is tossed three times. What is the probability that the same face will never appear two times n a row? Give an exact answer...
Suppose it costs $35 to roll a pair of dice. You get paid 5 dollars times the sum of the numbers that appear on the dice. What is the expected payoff of the game? Is it a fair game? Please show work so I can learn :) Thanks
4.54 Probability that sum of dice is a multiple of 4. Suppose you roll a pair of dice and you record the sum of the dice. What is the probability that the sum is a multiple of 4?
Suppose you roll a pair of fair 6-sided dice and place a bet on the sum. Which number would you select? (justify!)
You toss a pair of fair six-sided dice 30 times. What is... The probability that none of the 30 throws give a total of 12? The probability that a total of 7 appears 5 or more times?
Problem 1 (10 points). If two fair dice are rolled 10 times, what is the probability of at least one 6 (on either die) in exactly five of these 10 rolls? (Hint: For each roll, two dice are rolled at the same time. It is considered as the success if at least one of two dice is 6 and as the failure if neither of dice is 6.]
You roll a fair 6-sided dice, let Y be the outcome of the dice roll. Then conditioned on the event {Y = k} for k = 1, . . . , 6 you randomly choose, X, to be uniformly distributed between 0 and k. a) Use the law of total probability to compute P({X < x}). b) Use part a) to compute fx(x). c) What is the expectation of X.