Statistics 10              Lecture 9                    More Probability (14.1-14.3)

1.         Review

Definition. PROBABILITY is the study of CHANCE: a certain random process is given (such as rolling a die or spinning a roulette wheel), and we want to know the chance of various outcomes.

2.                Quick Review of Basic Rules

A.      The chance of something is the percentage of time it is expected to happen

B.      Chances are between 0% and 100%

C.     The chance of something is 100% minus the opposite thing  (the complement)

D.     Multiplying Probabilities: The chance that two or more things will happen equals the chance that the first will happen multiplied by the chance that the second happens and so forth given that a prior event does not forbid the occurrence of the future event.

3.      Calculating Basic Probabilities: 

       the number of outcomes of interest
       ---------------------------------- = probability of an event
       total possible number of outcomes  
 
Using this formula requires that you know how many outcomes to expect.  Example, Problem 7, Exercise Set C.  A coin is tossed 3 times.  What is the chance of getting at least 1 head?  You need to know what can possibly happen before you can estimate the chance of getting at least 1 (that means 1, 2, or 3) heads.

4.    Listing the Outcomes or Listing the Ways (14.1)

For some problems it might help you to list ways and it may help you to understand calculating chances.  If you toss a fair coin, you have two possible outcomes.

The chance of the coin landing heads up is 1/2. The chance of the coin landing tails up is 1/2.

Let's move to a situation where you are tossing a coin 3 times, there are 8 possible outcomes (2x2x2):

HHH HHT HTH HTT THH TTH THT TTT

When asked "what is the chance of getting 3 heads?" By listing the outcomes it's easy to see that it's 1/8. And if asked, "what is the chance of not getting 3 heads" it's easy to see that it's 7/8.

But listing outcomes may not be optimal it a situation like this one: you have 5 employees in your store. Employee A shows up 90% of the time, B shows up 75% of the time, C shows up 50% of the time, D shows up 90% of the time, and E shows up 60% of the time. What is the chance that at least one employee will be absent on a given day? Try listing the ways....(don't)

Instead, you might think about: Chance at least one absent = 100% - (chance of all 5 not absent)

5. Adding versus Multiplying Probabilities (14.2 and 14.3)

  1. Two events A and B are MUTUALLY EXCLUSIVE if the events A and B can't happen together.
  2. When asked to find the chance of at least one of two things (or more) things happening, ask if they are mutually exclusive. If they are, you can add the chances.
  3. Two events A and B are INDEPENDENT if knowing whether or not A happens does not help in predicting whether or not B happens. They can happen together, they just don't affect each other.