P(E and F)
This leads to conditional probabilities:
P(FE) = 
P(E)
P(drawing the first Ace) = 4/52 = 0.077
P(drawing a second Ace first Ace) = 3/51 = 0.059
The probability of F occurring , given the occurrence of event E is P(FE).
Rearranging this
equation gives us the general multiplication rule
(for any events, independent or not):
P(E and F) = P(E) • P(FE)
The probability of E and F occurring is P(E) occurring times P(FE) (probability of F
occurring given that E has occurred.
If E and F are independent
then P(FE) = P(F).
Note
:
in our problems we will be given all but one of the probabilities and then have to
use the equations to find the missing probability.
Sampling Rule of Thumb
:
with small random samples are taken from a large population
without replacements, if sample size is less than 5% of the population size, we can treat
events as independent.
Multiplication Rule of Counting
:
p•q•r• ….
For p choices of item 1, q choices of item 2, r
choices of item 3 and so on.
Permutations
:
order is important!
Combinations
:
order is not important
n! means (n) • (n1) • (n2) • (n3) • … • 2 • 1
(read n factorial)
Calculator can calculate factorials, permutations and combinations using math key and
PRB option.
Instructions on pg 306 of out text book.
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 Fall '12
 SonjaCox
 Probability, AP Statistics, Probability theory, Randomness, The Study of Randomness

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