Probability Calculator

If you leave P(A and B) blank, the joint probability is computed as P(A) times P(B), which is only correct when knowing that A happened tells you nothing about whether B happened. That holds for two separate coin flips. It does not hold for correlated events, and if you use it there, every downstream number (the or, the conditional) is wrong too. When you know the real joint probability, type it in.

Because adding them double-counts the outcomes where both happen. The formula subtracts the overlap: P(A) + P(B) - P(A and B). With two 60 percent events, naive addition gives 120 percent, which is nonsense; subtracting the 36 percent overlap gives 84 percent, which is correct under independence.

It is the ratio of failure to success, written as x : 1. A probability of 0.25 is odds against of 3 : 1, because three ways to lose for every one way to win. This is the convention used in betting, and it is why a quoted 3 : 1 corresponds to a 25 percent chance, not a 33 percent one.

No. The single-event section gives you one probability from counts, and the two-event section combines exactly two. For three or more you would chain the calculations yourself, and be careful: independence across a chain is an even stronger assumption than independence across a pair.

A total of zero or less, a negative count of favorable outcomes, or a favorable count greater than the total, each of which produces a specific error message rather than a silently wrong number. In the two-event section, a probability that resolves outside the range 0 to 1 is not accepted.