MCAT Physics and Math 12.4: Probability

Independent events do not impact each other, so their probabilities are never expected to change. If you roll a die and get a 3, then pick it up and roll it again, the probability of getting a 3 on the second roll is no different than it was before the first roll. Independent events can occur in any order without impacting one another.

Dependent events do have an impact on one another, such that the order changes the probability.

Mutually exclusive outcomes cannot occur at the same time. One cannot flip both heads and tails in one throw, or be both ten and twenty years old.

A group of outcomes is said to be exhaustive if there are no other possible outcomes. For example, flipping heads or tails are said to be exhaustive outcomes of a coin flip; these are the only two possibilities.

P(A ∩ B) = P(A and B) = P(A) × P(B)

P(A ∪ B) = P(A or B) = P(A) + P(B) − P(A and B)