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The Probability Calculator No Replacement For 3 calculates the probability of three sequential events occurring without replacement from a finite population. This is commonly used in statistics, probability theory, and various real-world applications involving dependent events.
The calculator uses the probability equation:
Where:
Explanation: The equation calculates the compound probability of three dependent events occurring in sequence, where each selection reduces the total number of available outcomes for subsequent events.
Details: Calculating probabilities without replacement is essential for understanding dependent events in statistics, quality control, risk assessment, and decision-making processes where outcomes are not independent.
Tips: Enter the number of favorable outcomes for each event and the total number of outcomes. All values must be non-negative integers, and total outcomes must be at least 3. Ensure favorable outcomes do not exceed available outcomes at each step.
Q1: What does "without replacement" mean?
A: Without replacement means that once an item is selected, it is not returned to the population, affecting the probabilities of subsequent selections.
Q2: When should I use this probability calculation?
A: Use this for scenarios where you're selecting multiple items from a finite set and each selection affects the remaining pool, such as card games, quality testing, or random sampling.
Q3: What are valid input ranges?
A: Total outcomes must be ≥3. Favorable outcomes must be ≥0 and cannot exceed the available outcomes at each selection step.
Q4: How is this different from probability with replacement?
A: With replacement, probabilities remain constant across selections. Without replacement, probabilities change as the population decreases.
Q5: Can this be extended to more than 3 events?
A: Yes, the pattern can be extended to any number of events by continuing the fraction pattern with decreasing denominators.