A single die is rolled four times. Find the probabilities that the number of 6s that appear is four.
A single die is rolled four times. Find the probabilities that the number of 6s that...
A fair die is rolled seven times. Calculate the probability of obtaining exactly two 6s. (Round your answer to four decimal places.)
3. (10 points) A fair, 6-sided die is rolled continually until two consecutive 6s appear. Find the expected number of rolls. (Hint: Ross Chapter 3, Exercise Q23)
Solve the problem involving probabilities with independent events. A single die is rolled twice. Find the probability of getting a 4 the first time and a 1 the second time. 36
A die is rolled four times. Find the probability of getting 5 exactly two times.
a) If a single six-sided die is rolled five times, what is the probability that a 6 is thrown exactly three times? b) A person receives an average of one e-mail message per half-hour interval. Assume that e-mails are received randomly in time, find the probabilities that in a particular hour 0,1,2,3,4,5 messages are received.
If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd.
A single six-sided die, whose faces are numbered 1 to 6, is rolled n times. The die is fair, each face is equally likely to land upward when the die is rolled. Let X be the number of times that the number on the upward face of the die is 1. Find the mean and the standard deviation of the random variable X.
Problem 6. A fair die is rolled four times. (a) Let Y denote the number of distinct rolls. Find the probability mass function of Y. (b) Let Z denote the minimal result fo the 4 throws. Find the probability mass function of Z
7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times 2 is rolled. Find the conditional distribution of X given Y-m 7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times 2 is rolled. Find the conditional distribution of X given Y-m
If a die is rolled six times, let X be then number the die obtained on the first roll and Y be the sum of the numbers obtained from all the rolls. Find the expected value and variance of x and y.