© Jill Zarestky
Math 141 Week in Review
Week in Review 6 Key Topics
7.1 Experiments, Sample Spaces, and Events
An experiment is an activity with an observable result.
• The result of the experiment is called the outcome or sample point.
• The set of all outcomes or sample points is called the sample space of the experiment.
o A sample space may be finite, in which case you can list all the elements.
o An infinite sample space has to be described and you can't list all the elements.
o A uniform sample space has equally likely outcomes.
• An event is a subset of a sample space.
Mutually Exclusive
• Events E and F are mutually exclusive if E ∩ F = ∅, that is, if E and F are disjoint.
7.2 Definition of Probability
Empirical Probability
• An estimate of the probability of an event based upon how often the event occurs after
collecting data or running an experiment with many trials.
• If the relative frequency approaches some value P(E) as the number of experiments n
increases, then P(E) is said to be the empirical probability.
Theoretical Probability
• Based on the sample space having equally likely outcomes.
• Find probability by using a sample space of equally likely outcomes.
• The probability of an event, P(E) is a number between 0 and 1.
o An event with probability 0 is impossible and an event with probability of 1 is
certain to occur.
Simple Events
• {s1}, {s2} . . . {sn} for a uniform sample space S = {s1, s 2, ..., sn}
• Simple events are mutually exclusive because only one can occur at a time.
• Then the probability of each of the simple events is P(s 1) = P(s2) = . . . = P(sn) =
•
1
n
.
The probability of each simple event is the same.
Probability Distribution
• Probability is assigned to each event.
• If S is the finite sample space of an experiment with n outcomes where each of the simple
events are mutually exclusive from each other, then
1. 0 ≤ P(si) ≤ 1
2. P(s1) + P(s2) + . . . + P(sn) = 1
3. P({si} ∪ {sj}) = P(si) + P(sj)
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© Jill Zarestky
Math 141 Week in Review
7.3 Rules of Probability
Properties of the Probability Function
• P(E) ≥ 0 for any E
• P(S) = 1
• If E and F are mutually exclusive, P(E ∪ F) = P(E) + P(F)
• If E and F are any two events of an experiment, P(E ∪ F) = P(E) + P(F) – P(E ∩ F)
• P(EC) = 1 – P(E)
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