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I can not derive an useful conclusion from this information....Quote:
5. A penny, nickel and dime are tossed together 100 times. They turn up heads 59, 52, and 47 times, respectively. The penny and nickel were heads together 33 times, the penny and dime were heads together 21 times. What can be said about the number of times that all three coins were heads together?
Get a conclusion from the inclusion (exclusion principle)Quote:
Originally Posted by ehpoc
Hello, ehpoc!
This is the Venn Diagram from Hell (coming soon to a theater near you).
Quote:
5. A penny, nickel and dime are tossed together 100 times.
They turn up heads 59, 52, and 47 times, respectively.
The penny and nickel were heads together 33 times,
the penny and dime were heads together 21 times.
What can be said about the number of times that all three coins were heads together?
A Venn diagram is suggested.
. .
Let. .Let
From the given information, we can fill in the Venn diagram:
There is a total of 100 coins.Code:* - - - - - - - - - - - *
| |
| P |
| |
| * - - - - - - - + - - - *
| x+5 | | |
| | | |
| | 33-x | |
* - - - * - - - + - - - + | |
| | | | | |
| | 21-x | x | | |
| | | | | 19-a |
| * - - - + - - - + - - - * |
| | | |
| | a | N |
| 26-a | | |
| * - - - + - - - - - - - *
| |
| D |
| |
* - - - - - - - - - - - *
. .
Hence: .
From the center region,, and the three adjacent regions,
. . we have: .
From [2]: .
Therefore: .