Question

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 25 trials and got the following results.Outcome 0,1,2,3,4,5,6,7,8,9Number of Trials 4,1,4,2,5,1,4,1,2,1Fill in the table below. Round your answers to the nearest thousandth.A - From these results, compute the experimental probability of getting a 2 or 6.B - Assuming that the machine is fair, compute the theoretical probability of getting a 2 or 6.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.

Answer 1

Outcome 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Number of Trials 4, 1, 4, 2, 5, 1, 4, 1, 2, 1

Experimental probability = actual number / total number

We got 4 of the number 2 balls and 4 of the number 6 balls = 8 balls in 25 picks

P( 2 or 6) = 8/25 =.32

Theoretical probability = expected outcome/ total outcome

There are 10 numbers , 2 of which are wanted ( 2,4)

P( 2 or 6) = 2/10 = 1/5 = .2

The experimental probability will get closer and closer to the theoretical probability with more and more trials

If we did 1000 trials it would be closer.

:With a large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.