A new electronics store holds a contest to attract shoppers. once an hour someone in the store is chosen at random to play the music game. here's how it works: an ace and four other cards are shuffled and placed face down on a table. the customer gets to turn cards over one at a time, looking for the ace. the person wins $100 worth of free cds or dvds if the ace is the first card, $50 if it is the second card, and $20, $10, or $5 if it is the third, fourth, or fifth card chosen. what is the average dollar amount of music the store will give away?

Let the numbers 1, 2, 3, 4, 5 represent the positions of the cards on the table (suppose the cards are placed in 5 boxes, for instance). And suppose the customers turn over the cards in this order : first number 1, then number 2, and so on.

(You should have a table with 5 columns labelled 1, 2, 3, 4, 5, and put a tick in the appropriate column for each occurrence of that number. Numbers 6 to 9 or 0 are not of interest, so ignore them.)

Continue the simulation for as long as you wish - - I would think about 100 numbers in total should suffice.

The number of ticks in each column represents the number of times the ace occurred in that position.

I have just done a quick simulation of this type. and got frequencies of 9, 12, 10, 8, 11 for the five numbers (50 trials in total).

This means that the store would have given away

(9 x $100) + (12 x $50) + (10 x $20) + (8 x $10) + (11 x $5) = $1835 to 50 customers, an average of $36.7 per customer.

Note that the ace has a 1/5 chance of being in any of the five positions, so 1/5 of the time it should be in position 1, 1/5 in position 2, and so on. So in 100 trials, for example, the store should have had 20 winners of each of the prizes, so the average prize per customer would have been

(100 + 50 + 20 + 10 + 5) x 20/100 = (185 x 20) / 100 = $37