Geometric Probability
Sometimes actual trials are difficult or unreasonable to conduct. In these situations, you can estimate the experimental probability of an event by using a simulation. A simulation is a model of the event.
Testing On a multiple-choice test, each item has 4 choices, but only one choice is correct. How can you simulate guessing the answers? What is the probability that you will pass the test by guessing at least 6 of 10 answers correctly?
How do you simulate guessing one out of four?
You can pick at random from four numbers, specifying that one of them will be the “correct” answer.
Think | write | |
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Randomly generate 1, 2, 3, or 4 ten times. Let 1 represent a correct guess. Then 2, 3, and 4 represent incorrect guesses. | Enter RANDINT (1, 4, 10) on a graphing calculator. Press
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The 10 outcomes represent 10 guesses on one test. Take the test 20 times. | 3431421212 | Three 1's. You scored 30%. |
Take the test 19 more times. | 3242431421 | |
4114113144 | 3431433434 | |
4412432243 | 4141441132 | |
2131241131 | 2143224113 | |
Look for tests that show 1 for at least 60% of the answers. | 1234312221 | 2111311214 |
4433323314 | 3242243214 | |
4314424244 | 3322213323 | |
2232224422 | 3233222413 | |
4112411124 | 2442122233 | |
3314222333 | 3223334334 | |
Only one test has at least 6 correct answers. The simulation shows | ||
Use the probability formula. |
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The set of all possible outcomes to an experiment or activity is a sample space. When each outcome in a sample space has the same chance of occurring, the outcomes are equally likely outcomes.
For one roll of a standard number cube, there are six equally likely outcomes in the sample space. You can calculate theoretical probability as a ratio of outcomes.