Probability

Probability = Number of desired or successful outcomes / Total number of possible outcomes

• All the outcomes must be equally likely - you can use a counting tree
• To determine the probability that independent events X and Y will both occur, multiply the two probabilities together.
• To determine the probability that mutually exclusive events X or Y will occur, add the two probabilities together.
  - if the events cannot occur together, add the probabilities of individual events
  - if the events can occur together, use the formula: P(A or B) = P(A) + P(B) - P(A and B)
• Probability of success + Probability of failure = 1
• If success contains multiple possibilities - especially if the wording contains phrases such as "at least" and "at most" - then consider finding the probability that success does not happen.
• Be careful of situations in which the outcome of the first event affects the probability of the second event, i.e. picking things out of a box.
• When you use a probability tree, multiply down the branches and add across the results.