Favorable outcomes
Three favorable outcomes among ten total outcomes gives 3/10 = 0.3 = 30%.
Calculate foundational probability relationships, compare events, evaluate repeated independent trials, and convert between probability and odds.
Probability describes how likely an event is on a scale from 0 (impossible) to 1 (certain). The same value can be written as a decimal, percentage, fraction, or odds.
These calculations describe mathematical models. Real-world results still depend on whether assumptions such as independence and constant trial probability are appropriate.
P(A) = favorable outcomes / total outcomesP(not A) = 1 − P(A)Use this multiplication rule only for independent events.
P(A and B) = P(A) × P(B)P(A or B) = P(A) + P(B) − P(A and B)P(A | B) = P(A and B) / P(B)P(at least one) = 1 − (1 − p)ⁿThree favorable outcomes among ten total outcomes gives 3/10 = 0.3 = 30%.
For P(A)=0.5 and P(B)=0.2, P(A and B)=0.5×0.2=0.1, or 10%.
For P(A)=0.4, P(B)=0.3, and an intersection of 0.1, the union is 0.6, or 60%.
With p=0.2 over three independent trials, 1−0.8³=0.488, or 48.8%.
Choose Decimal or Percentage explicitly; 0.25 and 25% represent the same probability.
Multiplying P(A) and P(B) assumes the occurrence of one event does not change the probability of the other.
AND asks for both events; OR includes either event and subtracts overlap to avoid counting it twice.
Probability compares successful outcomes with all outcomes. Odds in favor compare successful outcomes with unsuccessful outcomes. A probability of 0.75 corresponds to odds of 3:1 in favor.
Conditional probability restricts attention to outcomes where the condition occurred. An independence comparison checks whether entered values agree with P(A and B)=P(A)P(B), but rounded values cannot prove independence.
Probability is a number from 0 to 1 describing the likelihood of an event.
For equally likely outcomes, divide favorable outcomes by total possible outcomes.
The complement is the probability that an event does not occur: 1 minus its probability.
AND means both events occur. Independent event probabilities can be multiplied.
OR means at least one event occurs; subtract their overlap to avoid double counting.
It is the probability of one event given that another event has occurred.
Events are independent when one event does not change the probability of the other.
Subtract the probability of no successes from 1.
Probability compares success with all outcomes; odds compare success with failure.
No. A valid probability ranges from 0 to 1, or 0% to 100%.