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
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
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.
Suppose that you roll 112 fair six-sided dice. Find the probability that the sum of the dice is less than 400. (Round your answers to four decimal places.)You may need to use the appropriate table in the Appendix of Tables to answer this question.
A fair pair of dice is rolled 36 times. Find the probability that the same point comes up on both dice at least 11 times