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 1 2 3 4 6 7 8. 9. Number of Trials 42 47 45 54 48 45 55 54 64 46 Fill in the table below. Round your answers to the nearest thousandths. (a) From these results, compute the experimental probability of getting a 5 or 9. (b) Assuming that the machine is fair, compute the theoretical probability of getting a 5 or 9. (c) Assuming that the machine is fair, choose the statement below that is true: The smaller the number of trials, the greater the likelihood that the experimental probability will be close to the theoretical probability. The experimental probability will never be very close to the theoretical probability, no matter the number of trials. The larger the number of trials, the greater the likelihood that the experimental probability O will be close to the theoretical probability.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
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Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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O PROBABILITY
Experimental and theoretical probability
K
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
1
3
4
5
6.
7
8
Number of Trials
42
47
45
54
48
45
55
54
64
46
Fill in the table below. Round your answers to the nearest thousandths.
(a) From these results, compute the experimental probability of getting a 5 or 9.
(b) Assuming that the machine is fair, compute the theoretical probability of getting a 5 or 9.
(c) Assuming that the machine is fair, choose the statement below that is true:
The smaller the number of trials, the greater the likelihood that the experimental probability
O will be close to the theoretical probability.
The experimental probability will never be very close to the theoretical probability, no matter
the number of trials.
The larger the number of trials, the greater the likelihood that the experimental probability
O will be close to the theoretical probability.
Explanation
Check
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Transcribed Image Text:O PROBABILITY Experimental and theoretical probability K 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 1 3 4 5 6. 7 8 Number of Trials 42 47 45 54 48 45 55 54 64 46 Fill in the table below. Round your answers to the nearest thousandths. (a) From these results, compute the experimental probability of getting a 5 or 9. (b) Assuming that the machine is fair, compute the theoretical probability of getting a 5 or 9. (c) Assuming that the machine is fair, choose the statement below that is true: The smaller the number of trials, the greater the likelihood that the experimental probability O will be close to the theoretical probability. The experimental probability will never be very close to the theoretical probability, no matter the number of trials. The larger the number of trials, the greater the likelihood that the experimental probability O will be close to the theoretical probability. Explanation Check 22021 McGraw-Hill Education, All Rights Reserved. Terms of Use Privacy Accessibility
Expert Solution
Step 1

From the table we see that 5 came 45 times and 9 came 46 times.So 5 or 9 came total (45+46)=91 times.Given that the total number of trials= 500So the experimental probability is=n(5 or 9)n(all trials)=91500=0.182

 

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