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 41 40 50 64 59 43 51 52 50 50Fill in the table below. Round your answers to the nearest thousandth.(a) Assuming that the machine is fair, compute the theoretical probability of getting a 1.(b) From these results, compute the experimental probability of getting a 1.(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 a large difference between the experimental and theoretical probabilities.With a large number of trials, there must be no 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.

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

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

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.

Single choice10)What is the fair price of a lottery ticket that pays off $1,000 with a probability of 10% or zero with a probability of 90%?$100$900$500