Understanding Probability Calculations
Probability measures the likelihood of an event occurring. It's expressed as a number between 0 (impossible event) and 1 (certain event), often also shown as a percentage. This calculator helps determine basic probabilities.
Calculating Single Event Probability (P(A))
This is the most basic form. You need:
- Number of ways the specific event (A) can happen (favorable outcomes).
- Total number of possible outcomes.
Formula: P(A) = (Number of Favorable Outcomes for A) / (Total Possible Outcomes)
Example: Probability of rolling a '4' on a standard 6-sided die. Favorable outcomes = 1 (rolling a 4). Total outcomes = 6. P(rolling a 4) = 1 / 6 ≈ 0.1667 or 16.67%.
Probability of A OR B (Mutually Exclusive Events)
This calculates the chance that *either* event A *or* event B happens, assuming they **cannot** both happen at the same time (mutually exclusive).
Formula: P(A or B) = P(A) + P(B)
Example: Probability of rolling a '2' OR a '3' on a die. P(2) = 1/6, P(3) = 1/6. P(2 or 3) = 1/6 + 1/6 = 2/6 = 1/3 ≈ 0.3333 or 33.33%.
*(Note: If events *can* overlap, the formula is P(A or B) = P(A) + P(B) - P(A and B). This calculator uses the simpler mutually exclusive formula.)*
Probability of A AND B (Independent Events)
This calculates the chance that *both* event A *and* event B happen, assuming the outcome of event A **does not** affect the outcome of event B (independent).
Formula: P(A and B) = P(A) * P(B)
Example: Probability of flipping heads on a coin AND rolling a '6' on a die. P(Heads) = 0.5, P(Rolling a 6) = 1/6. P(Heads and 6) = 0.5 * (1/6) ≈ 0.0833 or 8.33%.
*(Note: If events are *dependent*, the formula is P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of B happening *given* that A has already happened.)*
This calculator provides tools for these fundamental probability scenarios.