Download Probability Rules!.

PROBABILITY RULES!
Conditions for Valid Probability Models
 A probability must be a number between 0 and 1 (or 0% and
100%).
0  P(A)  1
 The sum of all the probabilities in a sample space must equal 1
(100%).

P( A)  1
sample
space
Probability Rules!
 Complement Event Rule:
P(not A) = 1 – P(A)
 Addition Rule for “either/or”:
P(A or B) = P(A) + P(B) – P(A and B)
(general form)
If A and B are disjoint events, then
P(A or B) = P(A) + P(B)
because P(A and B) = 0.
 Multiplication Rule for “and/both”:
P(A and B) = P(A) . P(B/A)
(general form)
If A and B are independent events, then
P(A and B) = P(A) . P(B)
because P(B/A) = P(B).
 Conditional Probability Rule:
P(B/A)=
P(A and B)
P(A)
PROBABILITY RULES!
Central Limit Theorem
The sampling distribution of 𝑥̅ is approximately normal, centered at µ,
𝜎
the population mean, with standard deviation
.
𝑛
√
Binomial Conditions




Two Outcomes, “Success” and “Failure”
Probability of Success = p
Probability of Failure = 1 – p
n = number of independent trials
Binomial Random Variable
Let X = number of successes in n independent trials, then
P( x  k )  nCk  p k  1  p 
  np
nk
  np(1  p)
If the expected number of successes and failures are both at least 10, then
the binomial distribution is approximately normal.