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Probability of Simple and Compound Events

Learn about the theoretical and experimental probability of simple and compound events. Explore the concepts of independent and dependent events using examples. Understand how to calculate probabilities using tree diagrams and the fundamental counting principle.

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Probability of Simple and Compound Events

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  1. Topic 10 Probability

  2. 7.9.1 Probability of Simple Events

  3. 7.9.2 Theoretical and Experimental Probability • Theoretical probability is the expected probability of an event occurring. • (What is expected to happen.) • Experimental probability is found using frequencies obtained in an experiment or game. • (What actually happened.)

  4. 7.9.3 Probability of Compound Events • A tree diagram or table is used to show all of the possible outcomes, or sample space, in a probability experiment.

  5. 7.9.5 Fundamental Counting Principle

  6. 7.9.6 Permutations • A permutation is an arrangement, or listing, of objects in which order is important. You can use the Fundamental Counting Principle to find the number of possible arrangements.

  7. Example 2: Find P(5,4) • (The first number is the number you start with, the second number is the number of factors) 5 * 4 * 3 * 2 = 120

  8. 7.9.7 Independent and Dependent Events • Independent events: when one event does not affect the outcome of the other event. • For example: flipping a coin • The probability of two independent events can be found by multiplying the probability of the first event by the probability of the second event. • P(A and B) = P (A) * P (B)

  9. Dependent events: If the outcome of one event affects the outcome of another event. • For example: you have a bag with blue and green marbles. You pick one marble, do not replace it, and pick another marble. • If two events, A and B, are dependent, then the probability of both events occurring is the product of the probability of A and the probability of B after A occurs. • P(A and B) = P (A) * P (B following A)

  10. Are these independent or dependent events?

  11. Are these independent or dependent events?

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