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13.6 Conditional Probability Formulas

13.6 Conditional Probability Formulas. I. Conditional Probability.

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13.6 Conditional Probability Formulas

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  1. 13.6 Conditional Probability Formulas

  2. I. Conditional Probability • A. The conditional probability of an even B in relationship to an event A is the probability that event B occurs given that event A has already occurred. The notation for conditional probability is P(B l A), read as the probability of B given A. • B. The formula for conditional probability is: • ***

  3. II. Examples • A. A math teacher gave her class two tests. 25% of the class passed both tests and 42 % of the class passed the first test. What percent of those who passed the first also passed the second test?

  4. B. A jar contains black and white marbles. Two marbles are chosen without replacement. The probability of selecting a black marble and then a white marble is 0.34, and the probability of selecting a black marble on the first draw is 0.47. What is the probability of selecting a white marble on the second draw, given that the first marble drawn was black?

  5. C. The probability that it is Friday and that a student is absent is 0.03. Since there are 5 school days in a week, the probability that it is Friday is 0.02. What is the probability that a student is absent given that today is Friday?

  6. D. A coin is tossed. If it shows heads, a marble is drawn from Box 1, which contains one white and one black marble. If it lands tails, a marble is drawn from Box 2, which contains two white and one black marble. Find: • a. P(black l coin fell heads) • b. P(white l coin fell tails)

  7. E. A die is tossed. Find P(less than 5 l even).

  8. F. A number is selected, at random, from the set {1, 2, 3, 4, 5, 6, 7, 8}. Find • a. P(odd) • b. P(prime l odd)

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