A die is a cube with six sides on which each side contains one to six dots. Suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded. The possible outcomes of the sample space S are listed as follows, where in each case the die on the left is blue and the one on the right is gray. S  =  {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36,       41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} Write the following event as a set. (Enter your answer in set-roster notation. Enter EMPTY or ∅ for the empty set.) The event that the numbers showing face up are the same. Compute the probability of E.

A box contains 10,000 tickets: 4,000 zeros and 6,000 ones. And 10,000 draws will be made at random without replacement from the box. Which of the following best describes the situation? Group of answer choices The number of 1’s is likely to be different from 6,000, but the difference is likely to be small when compared to 10,000 draws. The number of 1’s will be 6,000 exactly. The number of 1’s is very likely to equal 6,000, but there is also some small chance that it will not be equal to 6,000.

An urn contains 5 tiles, each containing one of the numbers from 1 to 5. An experiment consists of selecting a tile marking down its number then replacing it and selecting a second tile and marking down its number how many outcomes are in the same sample space for this experiment?

Harry has 4 coins. If Harry flips all the coins at once, how large is the sample space?

A random sample, without replacement, of three items is to be selected from a population of five items (labeled a, b, c, d, and e). List all possible different samples.

The CEO of a company wants to determine if taking the employees to a company retreat would boost their morale. He decides to use a random number table to survey a simple random sample of 50 of the 250 employees. Which of the following correctly labels the population of employees? 000–250 001–250 0–250 1–250

Given a population of N=72​, starting in row 29 of the table of random​ numbers, and reading across the​ row, select a sample of n=14 (Table Attached) For a population containing N=9834 individuals, what code number would be assigned for   The eighth person on the list would be assigned code number?          b.The eighty-eighth person on the list would be assigned code number?           c.The last person on the list would be assigned code number?

Role-playing games like Dungeons & Dragons use many different types of dice. Suppose that a four-sided die has faces marked 1, 2, 3, and 4. The intelligence of a character is determined by rolling this die three times and adding 2 to the sum of the spots. The faces are equally likely, and the three rolls are independent. What is the average (mean) intelligence for such characters?

Assume that the box contains 7 balls: 4 white, 2 green, and 1 blue. Balls are drawn in succession without replacement, and their colors are noted until both a white and a green ball have been drawn. How many outcomes are there in the sample space?

A die is a cube with six sides and each side contains one to six dots. Suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded. The possible outcomes of the sample space S are listed as follows, where in each case the die on the left is blue and the one on the right is gray. S  =  {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36,       41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} Write the following event as a set. (Enter your answer in roster notation. Enter EMPTY or ∅ for the empty set.) The event that the sum of the numbers showing face up is at least 9. Compute its probability.