Probability of Exactly One Event Occurring Given Probability of Events Calculator

Formula Used:

\[ P(\text{Exactly One}) = (P(A) \times (1-P(B)) \times (1-P(C))) + ((1-P(A)) \times P(B) \times (1-P(C))) + ((1-P(A)) \times (1-P(B)) \times P(C)) \]

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 events do not occur. This is useful in scenarios where we want to know the chance of a single specific outcome among multiple possibilities.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P(\text{Exactly One}) = (P(A) \times (1-P(B)) \times (1-P(C))) + ((1-P(A)) \times P(B) \times (1-P(C))) + ((1-P(A)) \times (1-P(B)) \times P(C)) \]

Where:

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

Explanation: The formula sums up three scenarios: only A occurs, only B occurs, and only C occurs.

3. Importance of Probability Calculation

Details: Calculating the probability of exactly one event occurring is important in risk assessment, decision-making, statistical analysis, and various fields including finance, engineering, and scientific research where understanding the likelihood of specific outcomes is crucial.

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 ≤ probability ≤ 1). The calculator will compute the probability that exactly one of these three events occurs.

5. Frequently Asked Questions (FAQ)

Q1: What if I have more than three events?
A: This calculator is specifically designed for three events. For more events, the formula becomes more complex and would require a different approach.

Q2: Can probabilities be expressed as percentages?
A: No, the calculator requires probabilities as decimal values between 0 and 1. Convert percentages to decimals by dividing by 100.

Q3: What if the events are not independent?
A: This formula assumes events are independent. If events are dependent, additional information about their relationships would be needed.

Q4: What does a result of 0 mean?
A: A result of 0 means it's impossible for exactly one event to occur given the provided probabilities.

Q5: What does a result of 1 mean?
A: A result of 1 means it's certain that exactly one event will occur given the provided probabilities.