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Probability

Probability. Probability refers to the chances of an event happening.Symbolize P(A) to refer to event A.. Values of Probability. All values are between 0 and 1. Write answers as 3 place decimals.If P(A) = 0, it means the event WILL NOT happen.If P(A) = 1, it means the event WILL happen.. Rel

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Probability

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    1. Probability Part I

    2. Probability Probability refers to the chances of an event happening. Symbolize P(A) to refer to event A.

    3. Values of Probability All values are between 0 and 1. Write answers as 3 place decimals. If P(A) = 0, it means the event WILL NOT happen. If P(A) = 1, it means the event WILL happen.

    4. Relative frequency approximation of probability Conduct an experiment a large number of times.

    5. Example Toss a coin 10 times, recording whether you saw a head or a tail. P(Head) = Class results P(Head) =

    6. Theoretical probability Based upon what should occur, if events are equally likely.

    7. Example If you toss a single coin, what is the probability of getting a head?

    8. Example A die is rolled. What is the probability that the number showing is greater than 2? What is the probability that the number showing is at least 2?

    9. Die roll continued What is the probability that the number showing is less than 2? What is the probability that the number showing is at most 2?

    10. Example A card is selected from a standard deck of cards. What is the probability that it is a King? What is the probability that it is a red card? What is the probability that is a club?

    11. Law of Large numbers If an experiment is repeated again and again, the relative frequency probability of an event tends to approach the theoretical probability.

    12. Complement of an event Symbolized: Represents the chances an event will not happen Found by:

    13. Example What is the probability for each, using complements: The card is not a king The card is not red The card is not a club

    14. Tree Diagram Used to show all of the possible outcomes of an experiment

    15. Example A couple plans on having 3 children. Assuming that the births are single births, make a tree diagram.

    16. Questions Find each probability: All 3 children are girls There is one girl There is at least one girl There is at most one girl

    17. Addition Rule for 2 events P(A or B) means P(event A happens OR event B happens OR they both happen) P(A or B) = P(A) + P(B) – P(A and B)

    18. Example A card is drawn from a deck of 52 cards. What is the probability that it is either a King or a Heart?

    19. Example A card is drawn from a deck of 52 cards. What is the probability it is a King or a Queen?

    20. Mutually Exclusive Two events are mutually exclusive if they can not both occur at the same time. P(A and B) = 0 P(King and Queen) =

    21. Tables to present data To test the effectiveness of a new drug, trials are conducted where some people get a placebo and others get the drug.

    22. Questions: If a patient is randomly selected, what is the probability that: The patient took the drug The patient found treatment effective The patient took the drug and it was effective The patient took the drug or it was effective

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