1. What is a Probability Calculator?

Definition: This calculator computes the probability of various scenarios involving two events A and B, assuming independence.

Purpose: It assists in understanding the likelihood of outcomes in games, experiments, or statistical analysis.

2. How Does the Calculator Work?

The calculator uses the following formulas (for independent events):

Steps:

• Input \( P(A) \) and \( P(B) \) as percentages.
• Select the desired probability scenario from the options.
• Validate: Probabilities must be between 0% and 100%.
• Calculate the selected probability using the appropriate formula.
• Convert to a percentage and round to 4 decimal places.
• Display the result or a table for all scenarios if "All" is selected.

3. Importance of Probability Calculations

These calculations are key for:

• Games and Gambling: Assessing combined event chances.
• Statistical Analysis: Predicting multiple event outcomes.
• Decision Making: Evaluating risks across scenarios.

4. Using the Calculator

Examples (P(A) = 50%, P(B) = 30%):

• A and B both occurring:
  • \( P(A \cap B) = 0.5 \times 0.3 = 0.15 \).
  • Result: 15.0000%.
• At least one of the events occurs:
  • \( P(A \cup B) = 0.5 + 0.3 - 0.15 = 0.65 \).
  • Result: 65.0000%.
• Exactly one of these events occurs:
  • \( P(\text{exactly one}) = (0.5 \times 0.7) + (0.5 \times 0.3) = 0.35 + 0.15 = 0.5 \).
  • Result: 50.0000%.
• Neither A nor B occurs:
  • \( P((A \cup B)') = 1 - 0.65 = 0.35 \).
  • Result: 35.0000%.
• A NOT occurring:
  • \( P(A') = 1 - 0.5 = 0.5 \).
  • Result: 50.0000%.
• B NOT occurring:
  • \( P(B') = 1 - 0.3 = 0.7 \).
  • Result: 70.0000%.

5. Frequently Asked Questions (FAQ)

Q: What if probabilities exceed 100%?
A: The calculation is invalid, and an error is displayed.

Q: Are A and B assumed independent?
A: Yes, the calculator assumes independence for all calculations.

Q: What does 'Neither' mean?
A: It’s the complement of at least one event occurring.

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