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Definitions 3.1
Events, Sample Spaces, and Probability
• Experiment: an act (or process of observation) that
leads to a single outcome (that cannot be
predicted with certainty)
• Sample point: the outcome of an experiment
• Sample space (of an experiment): the collection of
all sample points
• Event: a specific collection of sample points
• Probability of an event: calculated by summing the
probabilities of the sample points in the sample
space of that event.
Experiment: an act (or process of observation) that leads to a single outcome (that
cannot be predicted with certainty)
Sample point: the outcome of an experiment
Sample space (of an experiment): the collection of all sample points
Event: a specific collection of sample points
Probability of an event: calculated by summing the probabilities of the sample
points in the sample space of that event.
Consider the experiment where I flip two fair coins (one nickel,
one penny) and record the results.
What is the sample space?
Consider the event E where at least one Head
is flipped. What is the probability that E
occurs?
Probability of an event: calculated by summing the probabilities of the
sample points in the sample space of that event.
Tree diagram
1st coin
2nd
coin
To find the probability of a sample point, simply multiply along a path.
*only use tree diagram when there are separate processes!
AAMFT Study of
Divorced Couple (book)
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Perfect Pals – joint custody never fight (.12)
Cooperative Colleagues – occasional conflict (.38)
Angry Associates – frequent fighting (.25)
Fiery Foes – constant fighting (.25)
What is the probability that a divorced
couple experiences at least some
conflict/fighting?
Why can’t we use tree diagram?
We find two new coins that are NOT fair. The
1st coin comes up heads with P=4/5 and the
2nd coin comes up heads with P=2/3.
Reconsider the event E (at least one Head is
flipped). What is the probability that E
occurs?
Redraw the tree diagram!
Probability of an event: calculated by summing the probabilities of the
sample points in the sample space of that event.
Probability Rules
Let pi be the probability of sample point I
1. 0≤pi≤1 the probability of each sample point is between 0
and 1
2. ∑pi=1
the sum of the probabilities equals 1.
Steps for Calculating the
Probabilities of Events
1. Define the experiment (describe the process used
to make an observations and the type of
observation that will be recorded)
2. List the sample points
3. Assign probabilities to the sample points
4. Determine the collection of sample points
contained in the event.
5. Sum the sample point probabilities.