Conditional probability basics
An event is a subset of all possible outcomes (the sample space), and two events are independent if one occurring doesn't change the probability of the other; a two-way table of counts can help you check independence or find a conditional probability, like the probability of A given that B already happened, written P(A given B) = P(A and B) / P(B). The addition rule, P(A or B) = P(A) + P(B) - P(A and B), avoids double-counting outcomes that satisfy both events: for example, if P(A) = 0.3, P(B) = 0.4, and P(A and B) = 0.1, then P(A or B) = 0.3 + 0.4 - 0.1 = 0.6.
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