This is the required formula for probability. Here all six
numbers occurs, where i occurs
times, i = 1,2,3,4,5,6.
(24) Roll a fair die n times. Write a formula for the probability that all 6...
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
If you roll a fair die 3 times, what is the probability that all 3 rolls will come up a value less than 4?
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?
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
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
3. Roll a fair die 10 times. Call a number in 1, 2, 3, 4, 5, 6 a loner if it is rolled exactly once on the 10 rolls. (For example, if the rolls are 1 5 6 4 4 4 6 2 4 1, then 5 and 2 are the only loners) a. Compute the probability that at leas tone of numbers 1, 2, 3 is a loner.
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].
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...
Problem Page A fair die is rolled 6 times. What is the probability that a 6 is obtained on at least one of the rolls? Round your answer to three decimal places.
Probability and Random Processes for
Engineers
You roll a fair die twice: all 36 outcomes are equally likely. Let A be the event that the first roll is 1, 2, or 3. Let B be the event that the second roll is 6. Finally, let C be the event that the sum of the rolls is even. (a) Show that any two of A, B, and C are independent (b) Are A, B, and C independent? Derive your answer two...