Probability Calculator

Use our free Probability Calculator to find how likely an event is to occur. Enter the number of favorable outcomes and total possible outcomes to calculate probability instantly.

The calculator is useful for solving basic probability problems involving coins, dice, cards, random selections, experiments, and statistics.

How to Use the Probability Calculator

The number of favorable outcomes should not be greater than the total number of possible outcomes.

What Is a Probability Calculator?

A Probability Calculator is an online tool that determines how likely an event is to happen.

Probability ranges from 0 to 1:

• 0 means the event is impossible.
• 1 means the event is certain.
• Values between 0 and 1 show different levels of likelihood.

Probability can also be written as a percentage between 0% and 100%.

For example:

• 0.20 = 20%
• 0.50 = 50%
• 0.75 = 75%
• 1 = 100%

Our calculator makes it easier to find probability without performing the division manually.

Probability Formula

For outcomes that are equally likely, the basic formula is:

P(A) = Favorable Outcomes ÷ Total Possible Outcomes

Where:

• P(A) = probability of event A
• Favorable outcomes = outcomes that meet your condition
• Total outcomes = all possible outcomes

Example

A bag contains 10 balls:

• 4 red
• 3 blue
• 3 green

What is the probability of selecting a red ball?

Favorable outcomes:

4

Total possible outcomes:

10

Calculate:

4 ÷ 10 = 0.4

Convert the result to a percentage:

0.4 × 100 = 40%

The probability of selecting a red ball is 40%.

Probability of Two Independent Events

Two events are independent when the result of one does not change the probability of the other.

For independent events that must both happen, multiply their probabilities:

P(A and B) = P(A) × P(B)

Example

The probability of getting heads on one fair coin flip is:

1/2

To get heads twice:

1/2 × 1/2 = 1/4

Therefore, the probability of getting heads on both flips is:

25%

Probability of A or B

To calculate the probability that event A or event B occurs, use:

P(A or B) = P(A) + P(B) − P(A and B)

The shared probability is subtracted because it would otherwise be counted twice.

If the two events cannot happen at the same time, they are mutually exclusive. In that case:

P(A or B) = P(A) + P(B)

Complement Probability

The complement of an event is the probability that the event does not occur.

Use:

P(not A) = 1 − P(A)

For example, if the probability of rain is:

0.30

Then the probability of no rain is:

1 − 0.30 = 0.70

So:

• Probability of rain = 30%
• Probability of no rain = 70%

Together, the two probabilities equal 100%.

Probability of At Least One Event

When an independent event is repeated several times, you may want to know the probability that it happens at least once.

Use:

P(at least once) = 1 − (1 − P(A))ⁿ

Where n is the number of attempts.

Example

Suppose the chance of success on one attempt is 20%, and you have 3 independent attempts.

Probability of no success:

(1 − 0.20)³ = 0.512

Subtract from 1:

1 − 0.512 = 0.488

The probability of getting at least one success is:

48.8%

Probability as a Percentage

To convert a decimal probability into a percentage:

Probability Percentage = Probability × 100

For example:

0.65 × 100 = 65%

To convert a percentage into decimal form:

65 ÷ 100 = 0.65

This makes it easy to move between decimal and percentage probability values.

Common Probability Examples

These examples assume that each possible outcome is equally likely.

Common Probability Calculation Mistakes

Using the Wrong Number of Outcomes

Make sure the total number includes every possible outcome.

For example, a standard six-sided die has 6 total outcomes, not just the outcomes you want.

Confusing Decimals and Percentages

A probability of:

0.20

means:

20%

Do not treat 20% as the number 20 when a probability formula requires decimal form.

Adding Instead of Multiplying

When two independent events must both happen, their probabilities are generally multiplied.

Forgetting Overlapping Events

When calculating A or B, shared outcomes may need to be subtracted to avoid counting them twice.

Assuming Events Are Independent

Not every pair of events is independent.

For example, when drawing cards without replacement, the first draw changes the number of cards available for the second draw.

FAQs

How to do probability in calculator?

For basic probability, divide the number of favorable outcomes by the total number of possible outcomes.

For example, if 3 out of 10 outcomes are favorable:

3 ÷ 10 = 0.3

The probability is 0.3, or 30%.

You can also enter the values into our Probability Calculator to calculate the result automatically.

How to use binomial probability formula?

Use the binomial probability formula when there is a fixed number of independent trials, each trial has two possible outcomes, and the probability of success remains the same.

The formula is:

P(X = x) = C(n,x) × pˣ × (1 − p)ⁿ⁻ˣ

Where:

• n = number of trials
• x = desired number of successes
• p = probability of success

For example, it can be used to find the probability of getting exactly 3 heads in 5 independent coin flips.

How do I calculate probability?

Use:

Probability = Favorable Outcomes ÷ Total Possible Outcomes

If 5 out of 20 possible outcomes are favorable:

5 ÷ 20 = 0.25

The probability is 25%.

What is a Probability Calculator?

A Probability Calculator is a tool that finds the likelihood of an event using the number of favorable outcomes and total possible outcomes.

Can probability be greater than 1?

No. A valid probability must be between 0 and 1.

When expressed as a percentage, probability must be between 0% and 100%.

What does a probability of 0.5 mean?

A probability of 0.5 means the event has a 50% chance of occurring.

A fair coin landing on heads is a simple example.

How do I calculate the probability of two events happening?

If the events are independent, multiply the probabilities:

P(A and B) = P(A) × P(B)

For example:

0.5 × 0.5 = 0.25

The probability that both events happen is 25%.

What is the probability of an event not happening?

Subtract the probability of the event from 1:

P(not A) = 1 − P(A)

If:

P(A) = 0.25

then:

1 − 0.25 = 0.75

The probability that the event does not happen is 75%.

How do I calculate the probability of at least one success?

Find the probability that the event never happens and subtract that value from 1.

Use:

P(at least once) = 1 − (1 − p)ⁿ

where p is the probability of success per attempt and n is the number of independent attempts.