Download Section 6.2 Probability Models

Section 6.2
Probability Models
Sample Space
• The sample space S of a random phenomenon
is the set of all possible outcomes.
• For a flipped coin, the sample space is S = {H,
T}. For a child's sex it is S = {girl, boy}. For a
table of random digits it is S = {0,1,2,3,4,5,6,7,
8,9}.
• For a coin flipped and a die rolled it is S = {H1,
H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}.
This may also be written S = {H1, T1, H2, T2,
H3, T3, H4, T4, H5, T5, H6, T6}. A tree diagram
may help you determine all of the possible
outcomes.
Multiplication Principle
• If you can do one task in a number of ways and
a second task in b number of ways, then both
tasks can be done in a * b number of ways.
• If we wish to list the possible outcomes of the
sex of 4 children, we would list S = {GGGG,
GGGB, GGBG, GBGG, BGGG, ..., BBBB}. Note
that there would be 2x2x2x2 = 16 possible
outcomes. But, if we simply wanted to know the
number of girls, we would have a simpler
sample space, S = {0, 1, 2, 3, 4}.
“Event”
• An event is an outcome or a set of
outcomes of a random phenomenon. So,
an event is a subset of the sample space.
Probability Rules
1. The probability P (A) of any event A
satisfies 0 <= P (A) <= 1. Any probability
is a number between 0 and 1.
2. If S is the sample space of a probability
model, then P (S) = 1. All probabilities
together must have a probability of 1.
Probability Rules
3. The complement of any event A is the event
that A does not occur, written as AC. The
complement rule states that P (AC) = 1 - P (A).
The probability that an event does not occur is
1 minus the probability that the event does
occur.
4. Two events A and B are disjoint if they have no
outcomes in common and so can never occur
simultaneously. If A and B are disjoint, P (A or
B) = P (A) + P (B). This is the addition rule.