Concept explainers
(a)
To describe how you will carry out a simulation of this game using the random digit table.
(a)
Explanation of Solution
In the question it is given that five cards each with different symbol are shuffled and we choose one. If it is diamond we win. Thus, we will carry out a simulation of this game using the random digit table as labeling are assigned based on the order they appeared in the picture but it will be arbitrary. So, first we need numeric labels for each shape. As,
Since
(b)
To perform ten repetitions of your simulation.
(b)
Explanation of Solution
In the question it is given that five cards each with different symbol are shuffled and we choose one. If it is diamond we win. Thus, the payout per repetition will be the number of random numbers it took the amount of draws subtracted from
(c)
To find out what is the average number of cards you would need to draw to obtain a diamond.
(c)
Answer to Problem 25PT2
The average length of the simulation was
Explanation of Solution
In the question it is given that five cards each with different symbol are shuffled and we choose one. If it is diamond we win. Thus, the number of cards in each of our simulation was titled length. To find the average we would add up all the ten repetitions and divide by
(d)
To explain is this a fair game.
(d)
Answer to Problem 25PT2
Yes, this is a fair game.
Explanation of Solution
In the question it is given that five cards each with different symbol are shuffled and we choose one. If it is diamond we win. Thus, to answer this question, we will use the simulation results. In order to get a more accurate answer, we would want to increase the repetition sizes. While the numbers are sampled at random, the sample size is low enough that sampling error may be large. And the decision rule would be, if we draw on average of five cards per game, we would break even. Based on our simulation results, we drew about
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