Basic Probability Calculations - PowerPoint PPT Presentation

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Basic Probability Calculations

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Example: How many orders are possible if you select from 5 entrees, 3 desserts, and 2 drinks? ... Selections of subsets without regard to order ... – PowerPoint PPT presentation

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Title: Basic Probability Calculations


1
Basic Probability Calculations
  • Cafeteria Method
  • Multiplication rule
  • General Assignment Method
  • Combinations
  • Specific Assignment Method
  • Permutations
  • Partitioning Method
  • Permutations

2
Cafeteria Problems
  • Pick one from each menu to define a single
    combination
  • Assuming you must pick one from each category,
    you apply the multiplication rule
  • Example How many orders are possible if you
    select from 5 entrees, 3 desserts, and 2 drinks?
  • 532 30 orders
  • There are 30 different ways to make an order.

3
General Assignment Problems
  • Selections of subsets without regard to order
  • Example How many ways can we select 3 different
    books from a set of 12 different books?
  • Example How many ways can we assign 5 different
    teachers to participate in a summer training
    program if there are 2 openings?

4
Specific Assignment Problems
  • How many ways can we assign 3 students to
    position of president, vice president or
    secretary if there are six people in the club?
  • (n 6, r 3), permutations
  • Example Five different teachers are available to
    teach EGR 252 and EGR 312 this term. In how many
    ways can we staff the courses if each teacher is
    only allowed to teach one course?
  • (n 5, r 2), permutations

5
Partitioning Problems
  • Example 2.20
  • In how many ways can we assign 7 students to one
    triple and two double rooms during a conference?
  • (n 7, n1 3 n2 2 n3 2),
  • 210 permutations
  • Note that there are three partitions and the
    total number of partitions (beds) available
    (n1n2n3) the total number of students to be
    assigned (n).
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