Each week 100 customers get cards for a drawing. Ten of the cards are worth $200

Question

Each week 100 customers get cards for a drawing. Ten of the cards are worth $200, 10 are worth $100, 20 are worth $50, and the rest are worth $20. A manager draws cards at random, awarding the customers the amount specified on their card. The drawings continue until the store has given away more than $400. Estimate the average number of winners each week. Perform 10 trials using the random numbers below. Let 0-5 represent $20, 6-7 represent $50, 8 represent $100, and 9 represent $200.

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Explanation / Answer

Ou of the 100 cards, we have -

10 cards worth - $200 (numbered 9)

10 cards worth - $100 (numbered 8)

20 cards worth - $50 (numbered 6-7)

60 cards worth - $20 (numbered 0-5)

The manager draws cards until the store has given away more than $400. So, the maximum number of cards that can be drawn = (400/20) = 20. This is because the least amount is $20, so assuming that you get a $20 card each time, you will exhaust after 20 cards. So, lets make random sampling of 20 cards.

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Now from the given list of random variables, select series of 10 continous random numbers. You can draw the 10 continuous numbers from anywhere. Let's say we get following 10 series in 10 trials -

So, the payoff corresponding to each of them is as shown below -

Now, replace these random, numbers with their respective payoffs (in $) as shown below -

Now, get the cumulative values of each trials as shown -

So, you see that the number of cards for which the sum crosses $400 is -

5 for Trial 1

6 for Trial 2

7 for Trial 3

10 for Trial 4

6 for Trial 5

7 for Trial 6

9 for Trial 7

9 for Trial 8

6 for Trial 9, and

11 for Trial 10.

So, average number of cards that can be drawn is -

Average = (5+6+7+10+6+7+9+9+6+11)/10 = 7.6

Hence, approximately 8 winners can win each week.

Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Trial 7 Trial 8 Trial 9 Trial 10 8 9 8 5 5 1 0 4 2 5 5 2 8 0 3 7 2 6 2 4 3 1 6 3 9 4 5 2 8 6 9 7 2 7 8 9 5 8 9 5 8 4 0 0 3 6 2 8 6 5 3 9 3 4 9 5 5 7 2 5 9 6 9 6 1 9 4 4 2 0 1 5 4 2 9 2 9 3 4 2 9 9 4 8 9 1 8 3 2 2 9 2 0 8 3 2 4 1 9 8 3 1 2 7 5 8 5 7 0 9 5 2 5 4 7 8 7 9 8 6 7 8 5 3 3 6 5 4 5 2 3 8 2 3 0 2 0 6 4 2 0 6 5 1 9 0 3 5 6 4 9 2 4 7 2 3 7 5 5 2 2 0 9 9 1 9 0 5 5 9 1 3 8 3 7 4 4 0 5 0 7 9 4 0 4 4 6 2 0 8 4 4 5 5 9 0 2 2 2 5

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