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Section 3.3

Section 3.3. The Addition Rule. Mutually Exclusive Events. Two events A and B are mutually exclusive if A and B cannot occur at the same time. EX: Decide if the events are mutually exclusive:. The Addition Rule. The Probability that Event A OR Event B will occur is:

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Section 3.3

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  1. Section 3.3 The Addition Rule

  2. Mutually Exclusive Events • Two events A and B are mutually exclusive if A and B cannot occur at the same time.

  3. EX: Decide if the events are mutually exclusive:

  4. The Addition Rule • The Probability that Event A OR Event B will occur is: • P(A or B) = P(A) + P(B) – P(A and B) • If A and B are mutually exclusive, then: • P(A or B) = P(A) + P(B)

  5. EX: Find each Probability • A math conference has an attendance of 4950 people. Of these, 2110 are college profs and 2575 are female. Of the college profs, 960 are female. a) Are the events “selecting a female” and “selecting a college prof” mutually exclusive? b) The conference selects people at random to win prizes. Find the probability that a selected person is a female or a college prof.

  6. 18. You roll a die. Find each Probability • Rolling a 5 or a number greater than 3. • Rolling a number less than 4 or an even number. • Rolling a 2 or an odd number.

  7. Section 3.4 Additional Topics in Probability & Counting

  8. Permutation: … an ordered arrangement of objects. The number of different permutations of n distinct objects is n! n! = n(n – 1)(n – 2)(n – 3)….(3)(2)(1) NOTE: 0! = 1

  9. Permutations of n objects taken r at a time… • Notation: nPr • nPr = n! (n – r)! • ORDER MATTERS!!!

  10. EXAMPLES • 20. Eight people compete in a downhill ski race. Assuming that there are no ties, in how many different orders can the skiers finish? • A psychologist shows a list of eight activities to her subject. How many ways can the subject pick a first, second, and third activity?

  11. Distinguishable Permutations • The number of distinguishable permutations of n objects, where n1 are of 1 type, n2 are of another type, and so on… is: • n! (n1!) (n2!) (n3!) .. (nk!)

  12. EX • How many distinguishable permutations are there using the letters in the word ALPHA? • In the word COMMITTEE?

  13. Combinations A selection of r objects from a group of n objects is denoted nCr • nCr = n! (n – r)!r! ORDER DOES NOT MATTER!!!

  14. EX • A three person committee is to be appointed from a group of 15 employees. In how many ways can this committee be formed? • If 6 of the 15 employees are women, what is the probability that a randomly chosen 3-person committee is all women?

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