Reflect on the "Game at McDonald's" that begins Chapter 5, as it will quickly show you how the concept of probability is applied.

Now, strengthen your understanding of the following concepts and terms. Please define and explain how they are applied. In the first part of your initial post,

• Define probability and probability distribution.
• Provide two industry or organization examples when probability is used.
• Explain how probability is used to make business predictions.

GAME AT MCDONALD'S Several years ago. McDonald's ran a campaign in which it gave game cards to its customers. These game cards made it possible for customers to win hamburgers. french fries. soft drinks. and other last-limd items. as 1tvell as cash prizes. Each card had It] covered spots that could be uncovered by rubbing them with a coin. Beneath three of these spots were \"zaps." Beneath the other seven spots were names of prizes. two of which were identical. For example. one card might have two pictures of a hamburger. one picture of a Coke. one of French Fries. one of a milk shake. one of $5. one of $It'l. and three zaps. For this card the customer could win a ham- . burger. To vvin on any card. the customer had to uncover the two matching spots (which showed the potential prize for that card} before uncovering a zap; any card with a zap uncovered was automatically void. Assuming that the two matches and the three zaps were arranged randomly on the cards. what is the probability of a customer winning\".I We label the two matching spots M1 and M3. and the three zaps 3.. 32. and 3;. Then the probability of winning is the probability of uncovering MI and M3 before uncovering El. 33. or 33. In this case the relevant set of outcomes is the set oi" all orderings of MI. M3. 2.. 2;. and 33.. shown in the order they are uncovered. As far as the outcome of the game is concerned. the other ve spots on the card are irrelevant. Thus. an outcome such as M3. 114.. Z}. 2.. Z; is a winner. whereas M3. 33. 2.. MI. E} is a loser. Actually. the first of these would be declared a winner as soon as M. was uncovered. and the second would be declared a loser as soon as E: was uncovered. However. we show the whole sequence of M's and 2's so that we can count outcomes correctly. We then nd the probability of winning using an equally likely argument. Specically. we divide the number of outcomes that are winners by the total number of outcomes. It can be shown that the number of out' comes that are winners is 12. whereas the total number of outcomes is lit}. Therefore. the probability ofa winner is IZIIEU = (I. I. This calculation. which shows that. on average. I out of Hi cards could be wins ners was obviously important for McDonald's. Actually. this provides only an upper bound on the fraction of cards where a prize was awarded. Many customers threw their cards away without playing the game. and even some of the winners neglected to claim their prizes. So. for example. McDonald's knew that if they made llll cards where a milk shake was the winning prize. somewhat less than SUE\") milk shakes would be given away. Knowing approximately what their expected "losses" would be from win ning cards. McDonald's was able to design the game [how many cards of each type to print]I so that the expected extra revenue [from customers attracted to the game} would cover the expected losses