Calculate the union, intersection, and complement of two independent events, or the probability of a range under a normal distribution.
Enter P(A) and P(B) as values between 0 and 1.
Find the area (probability) between two bounds on a normal distribution curve.
Two events are independent if one occurring doesn't change the probability of the other. For independent events, the probability of both happening is just P(A) × P(B) — that's the intersection. The union (A or B or both) is P(A) + P(B) minus the intersection, since otherwise the overlap would be counted twice.
Many real-world measurements — heights, test scores, measurement errors — cluster around an average in a predictable bell-curve pattern. The normal distribution calculator converts your bounds into z-scores (how many standard deviations from the mean) and finds the area under the curve between them, which corresponds to the probability of a value falling in that range.
Then you need conditional probability — P(A and B) = P(A) × P(B|A), where P(B|A) is the probability of B given that A already happened. This calculator's "two independent events" tool assumes no such dependency.
Every normal distribution has a different mean and spread, but converting to z-scores (standard deviations from the mean) maps any of them onto the same standard normal curve, so one set of probability tables (or one formula) works for all of them.
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