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Probability

Probability. 13.4 Probability of Compound Events. Probability of Two Independent Events: If two events , A and B, are both independent, then the probability of both events occurring is… . P(A and B) = P(A)*P(B).

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Probability

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  1. Probability

  2. 13.4 Probability of Compound Events Probability of Two Independent Events: If two events, A and B, are both independent, then the probability of both events occurring is… P(A and B) = P(A)*P(B) Probability of Two Dependent Events: If two events, A and B, are dependent, then the probability of both events occurring is… P(A and B) = P(A) * P(B following A)

  3. 13.4 Probability of Compound Events Example of Independent Events: What is the probability of rolling a 4 on a die 3 times in a row? Roll 1 Roll 2 Roll 3 P(4) = P(4) * P(4) P(three 4s) = P(4) * = ≈ or 0.423%

  4. 13.4 Probability of Compound Events Example of Dependent Events: What is the probability of drawing 6 hearts from a deck of cards without replacement? Draw 1 Draw 2 Draw 3 Draw 4 Draw 5 Draw 6 * * * * * P(six hearts) = = ≈ or 0.008429%

  5. 13.4 Probability of Compound Events Example: Suppose the odds of the Sixers beating the Kings in Basketball was 5 : 2. What is the probability of the Sixers beating the Kings 4 times in a row? P(Sixers win) Odds = Game 4 Game 1 Game 2 Game 3 P(4 wins) = * * * = = ≈

  6. 13.4 Probability of Compound Events Example: A particular bag of marbles contains 4 red, 6 green, 2 blue, and 5 white marbles. What is the probability of picking a red, white, and blue marble, in that order? Pick 1 Pick 2 Pick 3 P(r,w,b) = * * P(r,w,b) = ≈ .0098 What would the probability be with replacement? Pick 1 Pick 2 Pick 3 P(r,w,b) = * * P(r,w,b) = ≈ .0081

  7. 13.4 Probabilityof Mutually Exclusive Events and Inclusive Events Mutually Exclusive Events: If two events, A and B, are mutually exclusive, then that means that if A occurs, than B cannot, and vice versa. Probability of Mutually Exclusive Events: If two events, A and B, are mutually exclusive, then the probability that either A OR B occurs is… P(A or B) = P(A) + P(B)

  8. 13.4 Probabilityof Mutually Exclusive Events and Inclusive Events Inclusive Events: If two events, A and B, are inclusive, then that means that if A occurs, B could also occur, and vice versa. Probability of Inclusive Events: If two events, A and B, are inclusive, then the probability that either A or B occurs is… P(A or B) = P(A) + P(B) – P(A and B)

  9. 13.4 Probabilityof Mutually Exclusive Events and Inclusive Events Example: A particular bag of marbles contains 4 red, 6 green, 2 blue, and 5 white marbles. If 3 marbles are picked, what is the probability of picking all reds or all greens? mutually exclusive event P(red or greens) = P(red) + P(green) = = = = ≈ = = ≈

  10. 13.4 Probabilityof Mutually Exclusive Events and Inclusive Events Example: Slips of paper numbered 1 to 15 are placed in a box. A slip of paper is drawn at random. What is the probability that the number picked is either a multiple of 5 or an odd number? inclusive event P(mult of 5 or odd) = P(mult of 5) + P(odd) – P(5 and odd) = = = ≈

  11. 13.4 Probabilityof Mutually Exclusive Events and Inclusive Events Example: Two cards are picked out of a standard deck. What is the probability of both cards being either face cards or clubs? inclusive event P(face or clubs) = P(face) + P(club) – P(face and club) = = = ≈ =

  12. 13.4 Probabilityof Mutually Exclusive Events and Inclusive Events Example: 4 coins are tossed. What is the probability of obtaining 2 heads or 1 tail? mutually exclusive event P(2 heads or 1 tail ) = P(2 heads) + P(1 tail) = = = = =

  13. 13.4 Probabilityof Mutually Exclusive Events and Inclusive Events In a particular group of hospital patients, the probability of having high blood pressure is , the probability of having arteriosclerosis is , and the probability of having both is Determine whether the events are mutually exclusive or mutually inclusive. What is the probability that a patient in this group has either high blood pressure or arteriosclerosis?

  14. Probability of Two Independent Events: P(A and B) = P(A)*P(B) Probability of Two Dependent Events: P(A and B) = P(A) * P(B following A) Probability of Mutually Exclusive Events: P(A or B) = P(A) + P(B) Probability of Inclusive Events: P(A or B) = P(A) + P(B) – P(A and B)

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