# Latest content was relocated to https://bintanvictor.wordpress.com. This old blog will be shutdown soon.

## Thursday, October 23, 2014

### notation tips for probability puzzles

* There are many alternative notations for "probability of A and B". I prefer p(A . B) -- good for hand writing and computers

* There are many alternative notations for "probability of not-A". I prefer p(A' ) -- good for computers. How about p(!A)? Alien to many mathematicians.

* Favor shortest abbreviations for event names. For example, probability of "getting two 6's in 2 consecutive dice tosses" should NOT be written as p(66), but as p(K) by denoting the event as K.
* Avoid numbers in event short names -- things like 2 Pr(3) very ambiguous. If feasible, avoid number subscripts too.
* Favor single letters including greek letters and Chinese characters. If feasible, avoid any subscript.

Venn diagram - good at showing mutual exclusion between 2 events.
tree diagram - good at showing cond prob between 2 events
tree diagram - good at showing independence between 2 events

Note -- Mutual exclusion => independence,  but not vice versa.

Independence is intuitive most of the time but can be non-intuitive when you are deep into a tough puzzle.

Independence can be counter-intuitive and not captured in tree diagrams. Let h denote "salary above 100,000"; f=female. The 2 events happen to be indie in one firm but not another. In general, we have to assume not-independent.

Tossing a coin in the morning vs afternoon. Toss Should be independent of timing, but actual observation may not prove it.