Say you roll a die 6 times. Which of the following results is more likely: A, B or neither? a) 111111 b) 261435 . PLEASE write out all steps and please explain how you got your answer
Solution :
Probability of obtaining any number (from 1 to 6), when we roll a fair 6 sided dice is 1/6.
Hence, probability for result (a) is given by,


Hence, probability of obtaining any results from (a) and (b) are same. It means both of the results (a and b) are equally likely.
Say you roll a die 6 times. Which of the following results is more likely: A,...
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?
Perform the indicated goodness-of-fit
test.
You roll a die 48 times with the following results.
a. test statistic
b. critical value
Use a significance level of 0.05 to test the claim that the die is
fair.
A fair 6-sided die is rolled three times. Which is more likely: a sum of 11 or a sum of 12? Answer the question by calculating the probabilities for both. Thint 1] There are multiple ways to solve this problem. You may list all the favorable permutations to get the sum. However, this might be tedious and more error-prone. An easier way is to list only the favorable combinations (i.e., 3 numbers regardless of their order), and then find out...
Suppose that you roll a seven-sided die 5 times for which the sides are labeled from 1 to 7 on each side. What is the probability that out of the 5 times you roll, that you obtain an odd number at least 3 times?
If you roll a die 100 times, what is the approximate probability that you will roll between 9 and 16 ones, inclusive? (Round your answer to two decimal places.) HINT [See Example 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?
(24) Roll a fair die n times. Write a formula for the probability that all 6 numbers appear in the n rolls.
Problem 1. (12 points) A fair 6-sided die is rolled three times. Which is more likely: a sum of 11 or a sum of 12? Answer the question by calculating the probabilities for both. [hint 1] There are multiple ways to solve this problem. You may list all the favorable permutations to get the sum. However, this might be tedious and more error-prone. An easier way is to list only the favorable combinations (i.e., 3 numbers regardless of their order),...
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
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].