Chapter 4.1 Good For

This assignment is due 48 hours after the Chapter Test is given.

• Good Fors' solutions can be turned in anytime before 5:00 PM two days after the Chapter Test.
• Good Fors are worth 10 points of extra credit each.
• Answers must be accompanied by valid reasoning. Just like the tests, the answer alone isn't enough!
• Please enter your solution in the text area at the bottom of this page. DON'T FORGET TO GIVE YOUR NAME!

The Italian physician, mathematician, and compulsive gambler Gerolamo Cardano (1501 - 1576) wrote one of the first books on probabilities in gambling. Also, Cardano is famous in the automobile industry for inventing the undercarriage suspension device for horse drawn carriages. This device was later adapted for use in automobiles by Henry Ford, who named it the universal joint. The universal joint in Europe is still called a cardan in honor of its inventor.

Many of Cardano's ideas on the laws of probabilities weren't widely recognized by the mathematics community until decades after his death. This was due in part to the close involvement probability had with gambling and the taking of chances. In fact, probability theory was not viewed as a serious branch of mathematics until World War II.

In Cardano's, The Book on Games of Chance, he made the following statement which seems intuitively obvious, but contains one of the few mistakes in his scientific work. He wrote, "On the cast of one die, the chances are equal that a given point will turn up at least once in three throws, or again that one of three points will turn up in one throw." It turns out that these two experiments do not produce the same probabilities. What are the two correct probabilities?

Don't forget to explain your answer as clearly as possible.

Please type LAST name:

Please type your Student ID Number:

I received no help from anyone on this assignment.