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The probability of independent events A and B occurring together refers to the likelihood that both events happen simultaneously. For independent events, the occurrence of one event does not affect the probability of the other event occurring.
The calculator uses the multiplication rule for independent events:
Where:
Explanation: This formula applies only when events A and B are independent, meaning the occurrence of one event does not influence the probability of the other event.
Details: Calculating joint probabilities is essential in statistics, probability theory, risk assessment, and decision-making processes where multiple independent factors contribute to outcomes.
Tips: Enter probabilities for events A and B as values between 0 and 1. Both values must be valid probabilities within this range.
Q1: What makes events independent?
A: Events are independent if the occurrence of one event does not affect the probability of the other event occurring.
Q2: Can this formula be used for dependent events?
A: No, for dependent events, you must use the formula P(A∩B) = P(A) × P(B|A) where P(B|A) is the conditional probability of B given A.
Q3: What if probabilities exceed 1?
A: Probabilities must always be between 0 and 1. Values outside this range are invalid and indicate an error in input.
Q4: How are probabilities typically expressed?
A: Probabilities can be expressed as decimals (0.25), fractions (1/4), or percentages (25%), but this calculator uses decimal format.
Q5: What's the difference between independent and mutually exclusive events?
A: Independent events can occur together, while mutually exclusive events cannot occur simultaneously. For mutually exclusive events, P(A∩B) = 0.