Empirical Probability

• This is used when we can't possibly know the entire sample space.
• We use some method to observe a number of outcomes.
• We much prefer theoretical probability.
• P(e) = number of times e is observed/ total observations
• We will be given a table of statistics to do these problems.
• Examples:

  56, page 634
  
      P(female) =  n(female)/n(total)
            = 16.8 / 29.3 = 57%   or .57
  58:
      P(35-44)  = 4.2/29.3 = 14%
  62:
      We need to find the total here:
         renters = 18.7 + 4.5 + 1 = 24.2
         owners = 11.7 + 2.8 + .3 =  14.8
         Total   39
  
         P(renter) = 24.2 / 39 = 62%
     

More probability

• 11.5 is a non-section if you understand the FCP, _nP_r and _nC_r.
• P(E) = n(E)/n(S)
• Examples:

  2 page 639
     a: 6! = 720
     b: 3 * 3 * 2 * 2 * 1 * 1 = 23
     c: 23/720 
  4:
     n(S)   = 7! = 5,040
     a: n(Ea) = 6! 
        P(Ea) = 1/7
     b: n(Eb) = 5!
        P(Eb) = 7x6/7!= 7/120
     c: 1/7!
     d: n(Ed) = 2*6!
        P(Ed) = 2/7
  
  6: does order matter in this problem?
     a: 11C4 = 330
     b: 6C4 = 15
     c: 15/330  = 1/22
  
  8: 30C5 = 142,506
     P(w) = 1/142,506 = .000007
     100 * P(w) = .0007
  
  14:
     a: 52C5 = 2,598,960
     b: 4C4 = 1 
     c: 4C1 = 4
     d: 4*1 = 4
     e: 2/26565
     

Probability involving Not

• Sometimes it is easier to compute the probability of an event not happening than it is to compute the probability of an event happening.
• P(E) + P(not E) = 1
• P(not E) = 1 - P(E)
• Examples:

  2: page 649
    P(3) = 1/52
    P(not 3) = 1-1/52 = 51/52
  
  4:
    P(club) = 13/52 = 1/4
    P(not club) = 1 - 1/4 = 3/4
    

Homework

P 634: 55 to 66 odd
P 639: 1 to 18 odd
P 649: 1 to 16 odd