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# s_m4 - STA 2023 Module 4 Probability Concepts Rev.F08 1...

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Rev.F08 1 STA 2023 Module 4 Probability Concepts

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Rev.F08 2 Learning Objectives Upon completing this module, you should be able to: 1. Compute probabilities for experiments having equally likely outcomes. 2. Interpret probabilities, using the frequentist interpretation of probability. 3. State and understand the basic properties of probability. 4. Construct and interpret Venn diagrams. 5. Find and describe (not E), (A&B), and (A or B). http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.
Rev.F08 3 Learning Objectives (cont.) 1. Determine whether two or more events are mutually exclusive. 2. Understand and use probability notation. 3. State and apply the special addition rule. 4. State and apply the complementation rule. 5. State and apply the general addition rule. http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.

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Rev.F08 4 What is a Random Phenomena? A random phenomenon is a situation in which we know what outcomes could happen, but we don’t know which particular outcome did or will happen. http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.
Rev.F08 5 What is a Sample Space? In general, each occasion upon which we observe a random phenomenon is called a trial . At each trial, we note the value of the random phenomenon, and call it an outcome . When we combine outcomes, the resulting combination is an event . The collection of all possible outcomes is called the sample space . http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.

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Rev.F08 6 Sample Space and Event http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. The probability of an event reports the likelihood of the event’s occurrence.
Rev.F08 7 Possible Outcomes for Rolling a Pair of Dice http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.

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Rev.F08 8 Probability Notation http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. Remember, each occasion upon which we observe a random phenomenon is called a trial . At each trial, we note the value of the random phenomenon, and call it an outcome . When we combine outcomes, the resulting combination is an event . The collection of all possible outcomes is called the sample space . If E is an event, then P ( E ) represents the probability that event E occurs . It is read “ the probability of E .”
Rev.F08 9 Probability of an Event http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. In this case, we can represent the probability of an event as P ( E ) = f / N .

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Rev.F08 10 Basic Properties of Probabilities http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. Again, the probability of an event reports the likelihood of the event’s occurrence. We write P ( E ) for the probability of the event E , and 0 ≤ P ( E ) ≤ 1.
Rev.F08 11 When thinking about what happens with combinations of outcomes, things are simplified if the individual trials are independent .

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s_m4 - STA 2023 Module 4 Probability Concepts Rev.F08 1...

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