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Chapter 12 PROBABILITY

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Chapter 12 PROBABILITY Counting, Combinations, Permutations, Probability, Binomial Theorem Fundamental Counting Principle Two events: one occurs m ways and the other ... – PowerPoint PPT presentation

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Title: Chapter 12 PROBABILITY


1
Chapter 12 PROBABILITY
REVIEW
  • Counting, Combinations, Permutations,
    Probability, Binomial Theorem

2
Fundamental Counting Principle
  • Two events one occurs m ways and the other
    occurs n waysThey occur together mn ways

EXAMPLE How many different 7 digit phone
numbers are possible if the first digit cannot be
0 or 1?
3
PERMUTATIONS
  • An ORDERING of n objects n!
  • Permutations of n objects taken r at a time
  • Permutations with repetition

4
Example Questions
  1. There are 8 movies you would like to see
    currently showing in theaters. In how many
    different ways can you see all 8 of the movies?

5
Example Questions
  • There are 8 movies you would like to see
    currently showing in theaters. In how many ways
    can you choose a movie to see this Saturday and
    one to see this Sunday?

6
Example Questions
  • Find the number of distinguishable permutations
    of the letters in
  • POPPY

7
Example Questions
  • Find the number of distinguishable permutations
    of the letters in
  • WATERFALL

8
COMBINATIONS
  • Selection of objects NO ordering
  • EXAMPLE How many 5-card hands are possible when
    using a standard deck?

9
BINOMIAL THEOREM
  • Pascals Triangle coefficients of the binomial
    expansion
  • Sum of the exponents in each term must add to the
    original power
  • EXAMPLE Expand (x-5)4

10
Pascals Triangle
  • Write Pascals Triangle to the ( )7 line

11
Example Questions
  • Expand (x - 5)3

12
Example MC Questions
  1. What is the coefficient of x5 in the expansion of
    (2x - 3)6?A) 6 B) -36 C) 192 D) -576 E)
    -1152

13
PROBABILITY
  • Probability
  • P(A or B) P(A) P(B) P(A and B)P(A and B)
    P(A) P(B)Complement P(A) 1 P(A)

14
Example MC Questions
  1. You have 6 best friends, but only 4 cupcakes. In
    how many different orders can you give four of
    your six best friends cupcakes?A) 4 B) 12 C)
    24D) 120 E) 360

15
Example MC Questions
  1. In how many ways can a 5 person committee be
    chosen from a group of 8 people?A) 15 B)
    40C) 56 D) 336E) 6720

16
Example MC Questions
  • Events A and B are independent, P(A)0.9 and
    P(B)0.4.
  • What is P(A and B)?A) 0.4 B) 0.9C)
    1.3 D) 0.36E) 3.6

17
Example MC Questions
  1. The table below shows the number of students that
    like mustard and ketchup with their
    food.What is the probability that students
    who eat hamburgers choose ketchup as their
    condiment?A) .2 B) 0.25 C) 0.28D) 0.4 E)
    0.14

Hamburger Hot Dogs Chicken Sandwich
Mustard 40 2 20
Ketchup 10 10 5
18
Example MC Questions
  1. What is the probability that in a family of 6
    children exactly three are boys? Assume a boy
    and girl are equally likely to occur.A) 1/3 B)
    1/2 C) 5/16D) 5/32 E) 5/64
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