Probability of Exactly One Event Occurring Calculator

Formula Used:

\[ P(\text{Exactly One}) = (P(A) \times P(B') \times P(C')) + (P(A') \times P(B) \times P(C')) + (P(A') \times P(B') \times P(C)) \]

Probability of Exactly One Event Occurring:

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1. What is the Probability of Exactly One Event Occurring?

The probability of exactly one event occurring calculates the likelihood that only one out of three events (A, B, or C) will happen, while the other two do not occur. This is useful in probability theory and statistics for analyzing mutually exclusive outcomes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P(\text{Exactly One}) = (P(A) \times P(B') \times P(C')) + (P(A') \times P(B) \times P(C')) + (P(A') \times P(B') \times P(C)) \]

Where:

\( P(A) \) — Probability of Event A occurring
\( P(B) \) — Probability of Event B occurring
\( P(C) \) — Probability of Event C occurring
\( P(A') \) — Probability of Event A not occurring (1 - P(A))
\( P(B') \) — Probability of Event B not occurring (1 - P(B))
\( P(C') \) — Probability of Event C not occurring (1 - P(C))

Explanation: The formula sums the probabilities of three mutually exclusive scenarios where exactly one event occurs and the other two do not.

3. Importance of Probability Calculation

Details: Calculating the probability of exactly one event occurring is important in risk assessment, decision making, and statistical analysis where we need to determine the likelihood of specific outcomes among multiple possibilities.

4. Using the Calculator

Tips: Enter probabilities for events A, B, and C as values between 0 and 1. All probabilities must be valid (0 ≤ P ≤ 1). The calculator will compute the probability that exactly one of these events occurs.

5. Frequently Asked Questions (FAQ)

Q1: What if the events are not independent?
A: This formula assumes events are independent. If events are dependent, additional information about their relationships is needed.

Q2: Can this formula be extended to more than three events?
A: Yes, the concept can be extended to more events by including more terms in the summation, though the calculation becomes more complex.

Q3: What is the range of possible values for this probability?
A: The probability ranges from 0 to 1, where 0 means impossible and 1 means certain.

Q4: How does this differ from the probability of at least one event occurring?
A: "Exactly one" means only one event occurs, while "at least one" means one or more events occur (which includes exactly one, exactly two, or all three).

Q5: What if I have probabilities for more than three events?
A: This calculator is specifically designed for three events. For more events, you would need a different formula and calculator.