The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 500 trials and got the following results.Outcome 0 1 2 3 4 5 6 7 8 9Number of Trials 57 59 46 46 50 47 38 52 55 50Fill in the table below. Round your answers to the nearest thousandth.(a) From these results, compute the experimental probability of getting a 5 or 8.(b) Assuming that the machine is fair, compute the theoretical probability of getting a 5 or 8.(c) Assuming that the machine is fair, choose the statement below that is true:With a large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.With a large number of trials, there must be no difference between the experimental and theoretical probabilities.With a large number of trials, there must be a large difference between the experimental and theoretical probabilities.

In a certain state's lottery, 40 balls numbered 1 through 40 are placed in a machine and eight of them are drawn at random. If the eight numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. In this lottery, the order the numbers are drawn in does not matter.Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket. Write your answer as a reduced fraction.

Susan rolled a number cube 20 times and got the following results.Outcome Rolled 1 2 3 4 5 6Number of Rolls 4 3 3 3 2 5Fill in the table below. Round your answers to the nearest thousandth.(a) From Susan's results, compute the experimental probability of rolling a 5 or 6.(b) Assuming that the cube is fair, compute the theoretical probability of rolling a 5 or 6.(c) Assuming that the cube is fair, choose the statement below that is true:With a large number of rolls, there must be no difference between the experimental and theoretical probabilities.With a large number of rolls, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.With a large number of rolls, there must be a large difference between the experimental and theoretical probabilities.

There is a very popular lottery in which a ticket is called a scratcher. In this lottery, 49% of the scratchers are winning ones. Suppose that we will take a random sample of 8 scratchers. Let p represent the proportion of winning scratchers from the sample. Consider the sampling distribution of the sample proportion p.Complete the following. Carry your intermediate computations to four or more decimal places. Write your answers with two decimal places, rounding if needed.(a)Find μp (the mean of the sampling distribution of the sample proportion).=μp (b)Find σp (the standard deviation of the sampling distribution of the sample proportion).=σp

A lottery director wanted to fairly choose four winners from a group of 41 participants.He assigned each participant a two-digit number from 01 to 41.(Let's consider "01", "02", etc. to be two-digit numbers.)He then selected the following line from a random number table.11548 55865 07304 47090 23637 57011 52861Starting from the left, he used the line above to form two-digit numbers as follows.11 54 85 ...Using this new list and starting from the left, he chose four two-digit numbers from 01 to 41.He skipped numbers he had already chosen, the number 00, and numbers greater than 41.The participants who were assigned these two-digit numbers were chosen.Which four participants were selected as the winners?Participant, Participant, Participant, Participant

Amanda rolled a number cube 40 times and got the following results.Outcome Rolled 1 2 3 4 5 6Number of Rolls 6 6 7 7 5 9Fill in the table below. Round your answers to the nearest thousandth.(a) From Amanda's results, compute the experimental probability of rolling a 4.(b) Assuming that the cube is fair, compute the theoretical probability of rolling a 4.(c) Assuming that the cube is fair, choose the statement below that is true:With a large number of rolls, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.With a large number of rolls, there must be no difference between the experimental and theoretical probabilities.With a large number of rolls, there must be a large difference between the experimental and theoretical probabilities.