Mathematics · pattern F, Dataset
Enter favourable and total outcomes for a single probability, then combine two independent events for and, or, and at least once.
P(A) = favourable ÷ total; P(A and B) = P(A)P(B); P(A or B) = P(A) + P(B) − P(A and B)
The multiplication rule shown assumes independence. The addition rule subtracts the overlap, which is what prevents double counting.
0.250000
Computing the probability of at least one success directly means summing many cases; computing the probability of none and subtracting from one takes a single step. That complement trick is the most useful technique in elementary probability, and it is what the last row above does.
If the number is not the part you are stuck on, that is what the service is for — a specialist who explains the working, not just the answer.
Arithmetic runs in double-precision floating point, so results beyond about fifteen significant figures are not exact. Where a question wants an exact fraction or surd, keep the exact form rather than a decimal.