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Appendix E. Backgammon Scenario Worksheet

Worksheet #1

Backgammon Scenario

This sheet will be your reference sheet from now on. Keep it in your Mathematics notebook at all times. It will be a great study guide for you whenever a quiz, test or homework question is assigned.

When calculating probabilistic outcomes on equally likely events, the following steps should be followed:

1. Ask yourself: "What are all the possible outcomes"? What this really means is that you need to analyze what your sample space consists of. An example of this is to look at a dime. There are only 2 possible events when it is flipped-either a head or a tail. Thus, the total number of outcomes with a dime is 2. First is to set up some kind of table system to help you keep track of all the possible events.

Total Possible Outcomes = ____________________

2. Now we know how many total possible outcomes can occur. Next, lets look at finding the probability of certain events. Probability is a number between 0 and 1 that describes the likelihood that an event will occur. Because it is between 0 and 1, we know that this will be a ratio:

Probability(of an event)= # of times an event occurs/total number of possible outcomes

In essence, what you are finding is the theoretical probability of an event or a value arrived at analyzing all possible outcomes and assigning probabilities based on that outcome.

In our problem we need to find out the "chances" or the probability of getting hit by the black chip. We either can move the chip 4 times, 3 times, 7 times or none at all.

On the following page you are required to show all the work that is being in class. Write small so that you can fit all that is necessary.

Note: When dealing with probabilities it is sometimes helpful to deal with percents as well. Here's a quick review of the formula to convert fraction to percents:

 percent %

=
part (is) 
 100  whole (of)

2a. To find the chance of getting hit on Moving 7:

Fraction= __________ Percentage=_______________

2b. To find the chance of getting hit on Moving 3:

Fraction= ________ Percentage=_________________

2c. To find the chance of getting hit on Moving 4:

Fraction= __________ Percentage= _________________

2d. To find the chance of getting hit when not moving:

Fraction =__________ Percentage= __________________

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