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Probability Chapter 11

Probability Chapter 11. 1. Computation of Probabilities Section 11.3. 2. Properties of Probabilities. If E is an impossible event, then P(E) = 0. The probability of any event is 0 ≤ P(E) ≤ 1. The probability of A or B is given by

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Probability Chapter 11

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  1. ProbabilityChapter 11 1

  2. Computation of ProbabilitiesSection 11.3 2

  3. Properties of Probabilities If E is an impossible event, then P(E) = 0. The probability of any event is 0 ≤ P(E) ≤ 1. The probability of A or B is given by P(AU B) = P(A) + P(B) – P(A ∩ B) For any two mutually exclusive events A and B, P(A U B) = P(A) + P(B); that is, P(A ∩ B) = 0. 3

  4. Examples: • A single ball is taken from an urn containing 10 balls numbered • 1 through 10. Find the probability that the ball chosen is • an odd-numbered ball or a ball with a number less than 5. • an even-numbered ball or an odd-numbered ball. 4

  5. Examples: A single card is drawn from a deck of 52 cards. Find the probability the card chosen is a. the king of hearts or a spade. the ace of hearts or an ace. the king of hearts or a picture card. 5

  6. Examples: Refer to the following table. Find the probability of having at least 1 person in line. more than 3 persons or fewer than 2 persons in line. 6

  7. Solutions: 7

  8. Examples: In solving the following problem, refer to table 11.4 on page 733. What is the probability that a person who is alive at age 20 will not be alive at age 60 if the person is a male? if the person is a female? 8

  9. Solutions: a. P( a male is not alive at age 60 | alive at age 20) b. P( a female is not alive at age 60 | alive at age 20) 9

  10. Examples: Refer to the following table. Find the probability that a form had no itemized deductions and was correctly filled out. was not filled out incorrectly. 10

  11. Solutions: 11

  12. Examples: If the P(A') = 0.24, the P(AUB) = 0.79, and the P(A∩B) = 0.19, find each of the following P(B – A) P(B') P(A – B) 12

  13. Solutions: P(A∩B) = 0.19 b A B P(AUB) = 0.79 a b c 0.57 0.19 0.03 a c b Because this is probability, compartments a, b, c, and d must total to one. Thus d = 1- 0.79 = 0.21 d 0.21 P(A') = 0.24 c d a. P(B – A) = 0.03 c = 0.24 – 0.21 = 0.03 b. P(B ') = 0.57 + 0.21 = 0.78 a = 0.79 – (0.19 +0.03) = 0.57 c. P(A – B) = 0.57 13 END

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