Probability Calculator

What is probability?

Probability measures how likely an event is to happen, on a scale from 0 to 1. A probability of 0 means it cannot happen, 1 means it is certain, and 0.5 means it is just as likely to happen as not. You can also read it as a percentage, so 0.5 is a 50% chance.

For equally likely outcomes, you simply count the outcomes you care about and divide by the total number of possible outcomes.

How to use this calculator

1. Enter the number of favorable outcomes, the outcomes that count as a success.
2. Enter the total number of possible outcomes.
3. Check that the total outcomes number is not zero and is at least as large as the favorable outcomes.
4. Read the probability as a fraction, decimal, or percent after the calculator computes it.

The formula explained

The formula computes the probability of an event by dividing favorable outcomes by total outcomes. This gives a value between 0 and 1, where 0 means impossible and 1 means certain.

• P(A) = the probability of event A
• favorable outcomes = the number of outcomes that match the event
• total outcomes = the number of all possible outcomes

Step by step method

1. Count how many outcomes make the event happen.
2. Count the total number of equally likely outcomes.
3. Divide favorable outcomes by total outcomes to get the probability.

Worked example

Problem. A bag has 5 red marbles and 15 blue marbles. What is the probability of picking a red marble at random?

1. Favorable outcomes, red marbles, are 5.
2. Total outcomes are 5 + 15 = 20.
3. Compute probability: \(P(\text{red}) = \frac{5}{20} = \frac{1}{4} = 0.25\).

Tips and common mistakes

• Make sure the favorable outcomes are part of the total outcomes, not added separately twice.
• This formula works best when each outcome is equally likely, like a fair die, a shuffled deck, or a random draw from a bag.

Frequently asked questions