Venn Diagrams and Probability Distributions

Venn Diagrams are used when an event can take on two probabilities. For example: "There are two students in statistics, 4 in english, and 5 in both." The key word "both" tells us to use the Venn Diagram. Create the Venn Diagram first, then use it to determine whatever probability the question is asking you for. Remember that anything that is "neither" goes on the outside.

A probability distribution is a chart of probabilities when the random variable, x, can take on many different values. It looks like this:

x           0     1     2     3     4
P(x)     .1    .2   .15   .1   .45

x is the random variable. The numbers next to it are the values that the random variable can be. For example, I could get into zero, 1, 2, 3, 4 car crashes per year. The bottom row P(x) tells us the probability associated with that value. For example, the probability of me getting into 2 car crashes is .15. The bottom row of probabilities must always sum to 1.