Binomial Probability

• This is a special case.
• It is very different from everything else we have done.
• A typical problem involves
  • The probability for a given event.
  • But the event is repeated a number of times.
  • And we want to know the probability that it will succeed a second number of times.
  • An egg distributor determines that the probability that any individual egg having a crack is 14%. If I purchase a dozen eggs, what is the probability that exactly three are cracked?
• This fits the following definition
  • There are n repeated independent trials (I select an egg)
  • Each trial is classified as success or failure (cracked or not)
  • The probability for success remains constant.
• P(x) = (_nC_x)p^x(1-p)^n-x
  • n is the number of trials (12)
  • x is the number of successes (3)
  • p is the probability of success.
  • The book uses q=1-p
• So for my problem, P(3) = (₁₂C₃)(.14)³(.86)⁹.
• Do some problems page 764