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 40 trials and got the following results. Outcome 0,1,2,3,4,5,6,7,8,9 Number of Trials 4,4,1,4,1,3,6,4,7,6 Fill in the table below. Round your answers to the nearest thousandth. (a) Assuming that the machine is fair, compute the theoretical probability of getting an even number. (b) From these results, compute the experimental probability of getting an even number. (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.

Answer 1

a) If the machine is fair, the probability of getting each number is equal. So in this machine, we have 5 odd numbers (1,3,5,7,9) and 5 even numbers (0,2,4,6,8). As the number of both odd and even numbers is equal, we can say that the probability of getting an even number is 0.500.

b) With the help of these results, the experimental probability of getting even =

Total number of trials = 40

Total number of even numbers = 4+1+1+6+7 = 19

So, the experimental probability of getting an even number = 19/40 = 0.475.

c) Assuming that the machine is fair, the statement that is true is “ With large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small”. So, statement 1 is the correct answer.

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