you roll a fair die 4 times
how many ways can you get at least one 3?
how many ways can you get at most two 3's?
you roll a fair die 4 times how many ways can you get at least one...
A person rolls a standard six-sided die 8 times. In how many ways can he get 3 fives, 4 sixes, and 1 two?
A six sided die is rolled three times independently. How many different ways can you get a sum of 11? sum of 12?
A person rolls a standard six-sided die 9 times. In how many ways can he get 3 fives, 5 sixes, and 1 two?
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...
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].
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 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?
You are to roll a fair die n=123 times, each time observing the number of dots appearing on the topside of the die. The number of dots showing on the topside of toss i is a random variable represented by Xi, i=1,2,⋯,123. (a) Consider the distribution of the random variable Xi. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll of this die. μXi= (at least one decimal)...
We roll two fair 6-sided dice. (1) What is the probability that at least one die roll is 6? (2) Given that two two dice land on different numbers, what is the conditional probability that at least one die roll is a 6? Thint] You may use the graphical approach (Lecture 5 slide 11-12) to help you solve the problem. Problem 4. (8 points) We deal from a well-shuffled 52-card deck. What is the probability that the 13th card is...
If you roll a fair die 3 times, what is the probability that all 3 rolls will come up a value less than 4?