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Coin flips
1. Coin flips
To determine the probability that an event happens, one needs to know the sample space.
2. Sample space
The sample space consists of all the possible outcomes of an event. The sample space should be
collectively exhaustive (contain all possibilities) and be
mutually exclusive (no overlap of outcomes).
What are the possible outcomes from flipping a coin?
3. Result of flipping a coin
What are the possible results of flipping a coin? Here is one result.
Here are two results of flipping a coin.
Are these the only possible results?
Can a coin land in the edge? Try it with a nickel.
Are these the only possible results?
What if the coin rolls off the table?
What if the coin disappears?
What if something else happens?
The value "
bottom" is used to indicate these other possibilities.
Here is a diagram including "
bottom".
In programming, the
Null value can be used to indicate "
bottom" or "
no value".
4. Strings
In Python:
The empty string is "".
The bottom value is None.
5. SQL
In SQL, NULL is the bottom value
In JavaScript, undefined is the bottom value
6. Information and statistics
The field of statistics has a deep connection to computer/information science though it may not be immediately obvious.
Flip a fair coin. What is the probability that it is heads?
If you say it is one half, then that is the probability to you. I can see the coin and to me it is either zero or one - I know what it is. Information has a "point of view".
The entire field of statistics is the concept of known and unknown information by an observer and determining a "best guess" at what the state of the actual information of interest.
Thus, a saying is that "statistics means nothing to a rock".
7. End of page