Chapter 11, Problem 30E

To determine

To find: On the basis of the given data , the average dollar amount of music the store would give away.

Explanation of Solution

The knowledge that an ace and four other cards are shuffled and placed face down on a table is given to us. The participant, aiming for the ace, flips cards over one at a time. If the ace is the first card, the person wins $100. $50 if the second card is the ace, $20 if the third card is the ace. $10 if the fourth card is an ace and $5 if the fifth card selected is an ace. We need to calculate the average number of dollars per game that will be given away.

In any of the five circumstances mentioned above, we need to calculate the likelihood that the ace will be selected.

The likelihood that the first card will be the ace is 1 out of 5 or 20 percent. out of 4 or 25 percent is the likelihood that the ace is the second card.

The likelihood that the third card will be the ace is 1 out of 3 or 33.3 percent. 1 out of 2 or 50 percent is the likelihood that the ace will be the fourth card.

The chance of the last card being the ace is 1 out of 1 or 100 percent.

Step 2

Now, by multiplying each dollar amount by the respective likelihood and adding the five findings together, we can measure the average dollar amount given away per game.

  $\begin{array}{c}\text{Average Doller Amount = \$100}\times \text{Probability +}\text{\$50}\times \text{Probability}+\$20\times \text{Probability }\\ \$10\times \text{Probability }+\$5\times \text{Probability }\\ =\$100\times 20\%+\$50\times 0.25\%+\$20\times 33.3\%\\ +\$10\times 50\%+\$5\times 100\%\\ =\$49.17\end{array}$

Therefore, $49.177 per game is the estimated dollar sum given away.