Imagine that you decide to cheat at dice. You get a standard six-sided die and where...
You get a standard six-sided die and where the one normally is you add some pips (dots on dice) to make the one into a five. So now this die has no one but two fives. What is the variance of the number of pips showing on the die?
A person rolls a standard six-sided die 9 times. In how many ways can he get 3 fives, 5 sixes, and 1 two?
A person rolls a standard six-sided die 8 times. In how many ways can he get 3 fives, 4 sixes, and 1 two?
Two fair six-sided dice are rolled. What is the probability that one die shows exactly three more than the other die (for example, rolling a 1 and 4, or rolling a 6 and a 3)
dice is unbiased. Throws independent.
Step 1. You roll a six-sided die. Let X be the (random) number that you obtain. Step 2. You roll X six-sided dice. Let Y be the total number (sum) that you obtain from these X dice. Find E[Y] rounded to nearest .xx.
If you add random variables (such as add four dice) the new distribution has a mean and standard deviation of X=X1+X4+X3+X4 The mean and standard deviation for a fair 6-sided die and 10-sided die are: d 3.5 X210 = 5.5 Sa1o 2.031 Problem 1: Let Y be the sum of rolling three 6-sided dice (Bd6) plus two 10-sided dice (2410) Sds - 1.7078 Y = 3d6 + 2d10 la) What is the mean and standard deviation of Y? 1b) Using...
You roll a pair of standard six–sided dice and record the largest of the two outcomes. Let X be random variable associated with the outcome of this experiment. (b) What is the probability mass function (PMF) of X? (c) What is the cumulative distribution function (CDF) of X?
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...
If you roll two fair sided six sided dice one time, what are the chances that those of the dice will come up a five?
. [8] A gambler suspects a six sided die is "loaded" meaning the center of mass of the die is not in the center but toward one face, thus shifting the probability of each face from 1/6 each to something else. In the course of 600 trials, she observes (122 "aces", 103 "twos.98 "threes 95 "fours", 105 "fives" and 77 sixes". On a die, the even and odd spots are on opposite sides so one way we could look at...