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.

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Presentation transcript:

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 1 st coin 2 nd 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) 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 1 st coin comes up heads with P=4/5 and the 2 nd 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? Probability of an event: calculated by summing the probabilities of the sample points in the sample space of that event. Redraw the tree diagram!

Probability Rules Let p i be the probability of sample point I 1.0≤p i ≤1 the probability of each sample point is between 0 and 1 2.∑p i =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.