12.10 Probability Using Combinations

• Do problems 9, 13, 18 and 23 page 813

12.11 Binomial Probability Formula

• The Binomial Probability Distribution describes the probability for outcomes of conducting yes/no experiment a number of times.
• If I flip a coin four times, what is the probability that I will get tails three times?
  • Draw all possible outcomes.
  • 1/4
• If I toss a die 3 times, what is the probability that two times the result will be a 1?
  • There are 216 possible outcomes (Why)
  • But the probability outcomes are
  • 11x 1x1 x11 = 1/6x1/6x5/6 + 1/6x5/6x1/6 + 5/6x1/6x1/6
  • In general, there are ₃C₂ different ways we can get the results we are interested in.
  • Each one has the same probability (1/6)²x(5/6)¹
• The Binomial Formula
  • P(1) = 1/6, P(!1) = 5/6
  • The events are independent.
  • The event has two possible outcomes, success or failure
  • The probability of success remains the same for each trial
  • P(x) = (_nC_x)p^xq^n-x
  • n is the number of trials.
  • x is the number of times the answer is yes
  • p is the probability of a yes in a single trial
  • q = 1-p, the probability of no.
• P(two ones out of three) = (₃C₂)1/6²5/6^3-2
• Do problems 5, 15, 17 and 20 page 822