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Probability

Independent events. Two events, A and B, are independent if the occurrence of one event does not affect the probability of the occurrence of the other.. Examples. Rolling a pair of diceTossing 2 coinsDrawing 2 cards from a deck if the first card is replaced before the second card is drawn. Dep

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Probability

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    1. Probability Part II

    2. Independent events Two events, A and B, are independent if the occurrence of one event does not affect the probability of the occurrence of the other.

    3. Examples Rolling a pair of dice Tossing 2 coins Drawing 2 cards from a deck if the first card is replaced before the second card is drawn

    4. Dependent events Two events, A and B, are dependent if the occurrence of one event does affect the probability of the occurrence of the other.

    5. Examples Drawing 2 cards from a deck of cards if the first card is not replaced before drawing the second card. Note: Without replacement is a clue that the events will be dependent.

    6. Multiplication Rule Independent Events P(A and B) = P(A) * P(B) Dependent events P(A and B) = P(A)*P(B|A) P(B|A) means probability of B assuming that A has happened. It is called a conditional probability.

    7. Example Two cards are drawn from a deck of cards. What is the probability that both are Kings, if a. The first card is replaced before drawing the second card b. The first card is not replaced before drawing the second card

    8. Example A bin contains 10 batteries, 2 of which are defective. Two batteries are drawn out, one at a time. What is the probability that both are defective if: a. The first is replaced before drawing the second b. The first is not replaced before drawing the second

    9. At least and At most for independent situations A drug is effective 90% of the time. It is administered to 2 different patients. Find each probability: a. Both are cured b. Neither are cured c. At least 1 is cured d. At most 1 is cured

    10. Finding conditionals on a table To test the effectiveness of a new drug, trials are conducted where some people get a placebo and others get the drug.

    11. Examples What is the probability that the patient took the drug given it was effective? What is the probability that the patient found treatment effective given it was the drug?

    12. Testing independence for a table Two events will be independent if P(B|A) = P(B)

    13. Example Are the events drug and effective independent or dependent?

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