To prepare for this Discussion, simulate this same experiment using a single, si

Question

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. The probability of rolling a 3 is 1/6 (assuming the die is fair). So in the long run we will see on an average one 3 in every 6 rolls. So to get 100 3's we need approximately 6 x 100 = 600 rolls.

2. In real life however the number of rolls can be much different as the value calculated above is justan average value. We may be lucky to get all 100 3's in much less rolls, or much more rolls may be needed. Also if the die is not fair the probability willbe differentso will the average.

3. Most probably we may not get the same result as every roll has chance associated with it. For instance say you have been lucky to roll your first 3 in one roll, the next one may take 10 rolls. So for rolling 100 3's you may get a different number of rolls every time.

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