You roll a fair 6-sided die 1000 times and determine your “score” by summing over all your rolls. What are the average, variance and standard deviation of your score for this game? What is the probability that you scored less than 3300? That you scored more than 3600?
You roll a fair 6-sided die 1000 times and determine your “score” by summing over all...
Suppose you are rolling a fair four-sided die and a fair six-sided die and you are counting the number of ones that come up. What is the probability that both die roll ones? What is the probability that exactly one die rolls a one? What is the probability that neither die rolls a one? What is the expected number of ones? If you did this 1000 times, approximately how many times would you expect that exactly one die would roll...
You roll a fair six-sided die 5 times. What is the probability that EXACTLY one of the rolls lands on 1 (round your answer to 2 decimal places)? 10 4/8
Suppose I asked you to roll a fair six-sided die 6 times. You have already rolled the die for 5 times and six has not appeared ones. Assuming die rolls are independent, what is the probability that you would get a six in the next roll? 1/6 1/2 5/6 0 1
Question 3 3 pts Matching problem [Choose] You roll a fair six-sided die 500 times and observe a 3 on 90 of the 500 rolls. You estimate the probability of rolling a 3 to be 0.18 Choose) You roll a fair six-sided die 10 times and observe a 3 on all 10 rolls. You bet the probability of rolling a 3 on the next rollis close to O since you have already had 10 3's in a row You assign...
We roll a fair 8-sided die five times. (A fair 8-sided die is equally likely to be 1, 2, 3, 4, 5, 6, 7, or 8.) (a) What is the probability that at least one of the rolls is a 3? (b) Let X be the number of different values rolled. For example, if the five rolls are 2, 3, 8, 8, 7, then X = 4 (since four different values were rolled: 2,3,7,8). Find E[X].
If you roll a fair die 3 times, what is the probability that all 3 rolls will come up a value less than 4?
Players A and B each roll a fair 6-sided die. The player with the higher score wins ¤1 from the other player. If both players have equal scores, the game is a draw and no one wins anything. i. Let X denote the winnings of player A from one round of this game. State the probability mass function of X. Calculate the expectation E(X) and variance Var(X). ii. What is the conditional probability that player A rolls , given that...
suppose you only have one fair 6-sided die. We will say that a success is if you roll a 5 or a 6. You roll the die over and over until you roll two successes in a row. What is the the expected number of times you must roll before you stop?
6. A fair six sided die is rolled three times. Find the probability that () all three rolls are either 5 or 6 (6) all three rolls are even (c) no rolls are 5 (d) at least one roll is 5 (e) the first roll is 3, the second roll is 5 and the third roll is even
John and Paul play the following game. They each roll one fair 6-sided die. John wins the game if his score is larger than Paul’s score or if the product of the scores is an odd number. Find the probability that John wins.