The theory of probability developed from a study of various games of chance by u

Question

The theory of probability developed from a study of various games of chance by using coins, dice, and cards. Processes such as flipping a coin, rolling a die, or drawing a card from a deck are called probability experiments. This week we will use classical probability to estimate an outcome, and then test that estimate using empirical probability.

Often when playing gambling games, or collecting items in cereal boxes, one wonders how long it will be before one achieves success. For example, imagine there are six different types of toys with one toy packaged at random in a cereal box. If a person wanted a certain toy, about how many boxes would that person have to buy on average before obtaining that particular toy? Of course, there is the possibility that the particular toy would be in the first box opened or that the person might never obtain the particular toy; although these would be considered rare instances.

To prepare for this Discussion, simulate this same experiment using a single, six-sided die. Choose a particular number—for example, 3. Roll the die until you get your number; that’s one “try.” Make a chart and title it “Tries vs Rolls” Keep rolling until your chosen number is rolled 100 times (100 “tries”), and use your “Tries vs Rolls” chart to Keep track of the number of total rolls needed to roll the number you select 100 times. Ask your friends or family members to help and have fun with you!

In your write-up, think about and answer these questions:

1. What did you expect the average to be (from classical probability)?

2. What accounts for the differences from what you expected?

3. Would we get the same thing if we rolled another 100 experiments with the same die?

Explanation / Answer

1) Average number of tries to get the selected number = 6

2) it cannot be expected to get the exact same average when we do the experimentin actual case, because the expected value is the average for infinite number of trials. As the number of trials increase, we tend to get the value closer to the expected value.

3) if we did the experiment again, wecannot expect the result to be exactly same as the first time.

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