What does the OR Probability Calculator do?

This calculator computes the probability that at least one of two independent events occurs, given the individual probabilities P(A) and P(B). It uses the formula P(A or B) = P(A) + P(B) - P(A)*P(B).

How do I use the OR Probability Calculator?

Simply enter the probability of event A (P(A)) and the probability of event B (P(B)) as decimals between 0 and 1. The calculator will instantly display the probability that either event A or event B (or both) occurs.

What if my probabilities are percentages?

You can enter percentages as decimals (e.g., 50% as 0.5). The calculator expects decimal inputs, so convert percentages by dividing by 100 before entering.

统计与概率

即时、私密且免费

OR Probability Calculator.

Calculate the probability that at least one of two independent events occurs.

设备端计算无需注册

输入数值

输入时结果会更新。

02 / 答案

P(A)

P(B)

probability

0.58

probabilityPercent

Results update automatically as you type.

Use Cases

Risk Assessment in Projects

Determine the overall risk of at least one of two independent risks materializing, helping in contingency planning.

Example: If risk A has 20% chance and risk B has 30% chance, the OR probability is 0.44.

Quality Control Testing

Calculate the probability that a product fails at least one of two independent quality checks.

Example: If check A fails 5% and check B fails 10%, the OR probability is 0.145.

Frequently Asked Questions

What does the OR Probability Calculator do?: This calculator computes the probability that at least one of two independent events occurs, given the individual probabilities P(A) and P(B). It uses the formula P(A or B) = P(A) + P(B) - P(A)*P(B).
How do I use the OR Probability Calculator?: Simply enter the probability of event A (P(A)) and the probability of event B (P(B)) as decimals between 0 and 1. The calculator will instantly display the probability that either event A or event B (or both) occurs.
What if my probabilities are percentages?: You can enter percentages as decimals (e.g., 50% as 0.5). The calculator expects decimal inputs, so convert percentages by dividing by 100 before entering.

Tips & Common Mistakes

Tips

Ensure P(A) and P(B) are between 0 and 1. If you have percentages, convert them to decimals (e.g., 25% = 0.25).
This calculator assumes the events are independent. If they are not independent, the result may be inaccurate.
The OR probability includes the case where both events occur, so it's always greater than or equal to each individual probability.
Use the result to inform decisions, but remember it's a theoretical probability based on your inputs.

Common Mistakes to Avoid

Entering percentages as whole numbers (e.g., 50 instead of 0.5) – always convert to decimal.
Assuming the calculator works for dependent events – it only works for independent events.
Forgetting that the OR probability includes the intersection (both events happening), so it's not simply P(A) + P(B).

Last updated: August 13, 2026