An impossible sum corrected
- Input
- P(A)=60%, P(B)=70%
- Expected output
- P(A∪B)=88%
Adding directly would give 130%, impossible; subtracting the independent intersection (42%) brings the result back inside [0,1].
Carregando ferramenta… / Loading tool…
probability of two events
The union of two events adds both probabilities and subtracts the intersection, P(A∪B) = P(A) + P(B) − P(A∩B), because adding without subtracting counts the overlap twice. Skipping that adjustment can even return a number greater than 1, a value no real probability can have.
Adding directly would give 130%, impossible; subtracting the independent intersection (42%) brings the result back inside [0,1].
(1/6)×(1/6)=1/36: the multiplication rule holds because the outcome of one die does not change the odds of the other.
0.3÷0.5: knowing B occurred raises A's chance from 0.5 to 0.6, information A's standalone probability does not capture.
Divide favorable outcomes by possible outcomes. Rolling a die, the chance of a 4 is 1 ÷ 6 ≈ 0.167 = 16.7%.
They are events that never happen together, so P(A∩B) = 0 and the union formula simplifies to P(A∪B) = P(A) + P(B), with nothing to subtract. Getting heads and tails on the same coin flip is an example: the two never occur at the same time.
They are independent when P(A∩B) = P(A)×P(B) checks out against the data, as with two separate dice, 1/6×1/6=1/36. If the real intersection differs from that product, the events have some dependence between them, and using the multiplication rule in that case underestimates or overestimates the intersection.
Because the plain sum counts the slice where both events happen at once, the intersection, twice; with P(A)=60% and P(B)=70%, the direct sum reaches 130%, impossible, and only subtracting the intersection (42% in the independent case) returns the correct value, 88%.
Calculations run in your browser. No data is sent to a server.