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 50 trials and got the following results.Outcome 0 1 2 3 4 5 6 7 8 9Number of Trials 5 3 7 6 4 4 3 10 4 4Answer the following. Round your answers to the nearest thousandths.(a)From these results, compute the experimental probability of getting a 1 or 5.(b)Assuming that the machine is fair, compute the theoretical probability of getting a 1 or 5.(c)Assuming that the machine is fair, choose the statement below that is true.

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.

Suppose a lottery ticket costs $1 and the probability that a holder will win nothing is 90%. What must the jackpot be for this to be a fair bet?Group of answer choices1,0001010,000100

Lisa rolled a number cube 25 times and got the following results.Outcome Rolled 1 2 3 4 5 6Number of Rolls 5 2 6 4 7 1Answer the following. Round your answers to the nearest thousandths.(a)From Lisa's results, compute the experimental probability of rolling an odd number.(b)Assuming that the cube is fair, compute the theoretical probability of rolling an odd number.(c)Assuming that the cube is fair, choose the statement below that is true.

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