- Complementary probabilities
- property of complements
- in favor
- find odds, given the probability
- find probability, given the odds
- Conditional probability
- procedure for using tree diagrams
13.3 Essential Ideas
PROPERTY OF COMPLEMENTS:
P(E) = 1 – P(E compliment)
Odds in favor of an event E :
s/f (ratio of good to bad)
Odds against an event E :
f/s (ratio of bad to good)
s = NUMBER OF SUCCESSES
f = NUMBER OF POSSIBILITIES
s + f = n
Suppose that you know P(E ) and wish to find the odds:
odds in favor of an event E :
P(E )/P(E compliment)
odd against on event E :
P(E compliment)/P(E )
Suppose that you know the odds in favor of an event E and wish to find the probability:
P(E ) = s/(s + f)
P(E compliment) = f/(s + f)
The fundamental counting principle gives the number of ways of two or more tasks. If task A can be performed in m ways, and if, after task A is performed, a second task B, can be performed in n ways, then task A followed by task B can be performed in mn ways.
The probability of an event E given that another event F has occurred is called a conditional probability, and is denoted by P(E | F).
The procedure for using tree diagrams:
Multiply when moving horizontally across a limb.
Add when moving vertically from limb to limb.
Conditional probabilities; start at their condition.
Unconditional probabilities; start at the beginning of the tree.