Introduction to Probability

What is probability? A number between 0 and 1 (inclusive) that gives us an idea of how likely it is that an event will occur. An event with a probability of 0 is an impossible or null event. An event with a probability of 1 is a sure thing or a certain event. Closer probability is to 1, more likely it is to happen.

Three Ways of Assigning Probabilities to Events Personal opinion approach Relative frequency (experimental) approach Classical (theoretical) approach

Personal Opinion Approach “Your guess is as good as mine” approach. Individual specifies probability based on his or her own experiences, knowledge, hunches, … Only constraint is that probabilities must make sense.

Relative Frequency Approach Observe something a large number of times. [“Toss a coin”] Count the number of times the event of interest occurs. [“# of heads”] Estimate probability of event by calculating the proportion of times the event occurred [“# of heads  # of tosses”]

Example: Relative Frequency Approach Tosser#(Tosses)#(Heads) P(H) Buffon 4,040 2, Pearson 24,00012, Kerrich 10,000 5, Note:To use this approach, you cannot observe process only a few times. Must be able to observe process enough to see what happens in “the long run”!

Classical Approach Approach only “legit” if each outcome is equally likely. Count total number of possible outcomes. (“52 cards”) Count number of ways the event can occur (“4 aces”) Divide # of event ways by # of total ways to get probability (P = 4/52 = 0.077)