Once upon a time, there was a powerful king. He wanted his daughter, Princess Sophie to marry a wealthy man with royal blood. With this in mind, he arranged a wedding with the neighboring king’s son, Prince Ernest. At first, Princess Sophie did not seem to oppose to the arranged marriage, however, as fate would have it, she met a young man in the village and fell in love with him. This man’s name was Solomon.
Princess Sophie pleaded with her father to cancel the arranged marriage so that she could marry Solomon, the man she loved. At first the king was furious. He wanted to throw Solomon to the lions. It took many hours of his beloved daughter’s begging to convince him to allow the following compromise.
The king demanded that Solomon enter a maze which led to two rooms. In one would be the fair Princess Sophie, and in the other would be lions…hungry lions!!!
Look closely at the maze below and decide in which room you would wait if you were Princess Sophie.
TI-73: APPS: 6: Prob Sim
Simulate the
experiment
20 times, and record in the table below the room in which he arrives.
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|
|
|
|
|
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| 1 | . | . | 11 | . | . |
| 2 | . | . | 12 | . | . |
| 3 | . | . | 13 | . | . |
| 4 | . | . | 14 | . | . |
| 5 | . | . | 15 | . | . |
| 6 | . | . | 16 | . | . |
| 7 | . | . | 17 | . | . |
| 8 | . | . | 18 | . | . |
| 9 | . | . | 19 | . | . |
| 10 | . | . | 20 | . | . |
According to your
experiments,
in which room should Princess Sophie wait if she wants the best chance
of marrying Solomon?
We can use a tree diagram to determine the theoretical probability of Solomon’s ending up in Room X or Room Y.
What is the
theoretical
probability of Solomon winding up in Room X?
What is the
theoretical
probability of Solomon winding up in Room Y?
Where should Princess
Sophie wait if she wants to have the best chance of marrying Solomon?
Even if Princess
Sophie
waits in the best room, is it still possible that Solomon will be eaten
by lions? Explain.
Updated: 08/21/2003
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