An experiment is rolling two dice. SS = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}   a. What is the probability of getting a 1st is 2 or a sum of 7? P(1st is 2 or sum of 7) =    Give your answer as a reduced fraction.   b. What is the probability of getting a sum of 3? P(sum of 3) =    Give your answer as a reduced fraction.

We roll 2 dice 4 times and we want to know the number of times the sum of the dice was 7. Find the distributionof probabilities.

A pair of dice is rolled. The outcomes are summarized in the following table: (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) 1. Find the probability, that the sum is 10 (adding the two numbers will equal to 10). Give your answer as a decimal, rounded to two decimal digits. 2.Find the probability, that the sum is more than 10 (which means 11 or 12). Give your answer as a decimal, rounded to two decimal digits. 3. Find the probability, that the sum is 6 OR the sum is more than 10. Give your answer as a decimal, rounded to two decimal digits. 4.Find the probability, that the sum is even. Give your answer as a decimal, rounded to two decimal digits. 5.Find the probability, that the sum is even AND the sum is more than 10. Give your answer as a decimal, rounded to two decimal digits.

students were assigned a quiz that contains 7 independent multiple-choice problems. Each problem was worth 1 point and has 4 choices, where only one of them is correct. A pirate, who does not understand probability and statistics, disguises himself as a clever student and tried to pass one of the quizzes. Unlike our students, he is not able to solve the problems and, thus, decides to randomly choose an answer for each problem. Let X be a random variable representing the score of the pirate on the FIRST problem of the quiz. What distribution does X follow?

A pair of dice is rolled. The outcomes are summarized in the following table: (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) 1. Find the probability, that the sum is 11 (adding the two numbers will equal to 11).  Give your answer as a decimal, rounded to two decimal digits. 2. Find the probability, that the sum is more than 10 (which means 11 or 12). Give your answer as a decimal, rounded to two decimal digits. 3. Find the probability, that the sum is 6  OR the sum is more than 10. Give your answer as a decimal, rounded to two decimal digits. 4.Find the probability, that the sum is even. Give your answer as a decimal, rounded to two decimal digits. 5.Find the probability, that the sum is even OR the sum is more than 10. Give your answer as a decimal, rounded to two decimal digits. 6.Find the probability,…

You're a sociologist studying whether grocery prices are different in the inner cities than they are in the suburbs. To investigate this, you pick a random set of items (a basket of goods), and then send shoppers to buy these items at an inner city (IC) grocery, and also at a suburban (SU) grocery. You pick 30 different baskets of goods, so your secret shoppers buy 30 baskets, once at the inner city store, and once at a suburban store.The data is given in the dataset named "ICvSU_3095.xls", which you can find in data folder under Course Documents.  Prices could be higher in the inner city because of discrimination, or they could be higher in the suburbs because of the greater disposable income. Use Excel to test the research hypothesis that inner city prices are different than the suburb's prices. The null hypothesis is that inner city prices are equal to suburban prices. You test at the alpha = 0.05 significance level.  What do you conclude? Are prices the same? Who has higher prices?…

Suppose that we roll three (six-sided) dice 600 times. Find an approximation for theprobability that we obtain the “triple-one” combination (each dice showing the value 1)at most 3 times.

1) Rolling two four-sided dice, what's the likelihood of getting the same sum twice in a row?