Probability calculator

This calculator computes the probability of a selected event based on the probability of other events. The calculator uses the addition rule, multiplication rule, and Bayes theorem to find conditional probabilities.The calculator generates a solution with a detailed explanation.

Two events Series of events

For dependent events enter 3 values. For independent events input 2 values.
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Solve for

Provide any three known values.

P( A ) =

P( B ) =

P( A and B ) =

P( A or B ) =

P( A | B ) =

P( B | A )

Events A and B are

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Probability calculator

probability of k successes in n trials – binomial probability
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Let the probability of event A be P(A) =
If we repeat an experiment times, what is the probability that event A will occur times?

Example: The probability of getting head is 0.5. If a coin is tossed 5 times, what is the probability of getting exactly 2 heads?

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Examples

ex 1:

A single card is chosen from a deck of 52 playing cards. What is the probability of choosing an ace or a heart?

ex 2:

A fair six sided die is rolled. What is the probability of rolling a number divisible by 3, or an even number?

ex 3:

Find the probability of getting exactly 6 heads in 10 tosses.

ex 4:

Find the probability of getting more than 8 heads in 10 tosses.

ex 5:

If a player scores 3 out of 5 free throws, what is the probability that he will score more than 9 out of 12 attempts?

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Find more worked-out examples in our database of solved problems.

TUTORIAL

Basic Rules for Finding Probabilities

The addition rule is used to find the probability that event A or event B occurs. To apply this rule, we need to add probabilities for events A and B and then subtract the probability of intersection. So for the union of two events, we have the following formula:

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

Example 1: Consider families with two children. Let A be the event that the first child is a girl, and B be the event that the second child is a girl. In this case, P(A and B) is the probability that both children are girls, and P(A or B) is the probability that at least one child is a girl. If we know that P(A) = 1/2, P(B) = 1/2, and P(A and B) = 1/4, then:

P(A or B) = P(A) + P(B) - P(A and B) = 1/2 + 1/2-1/4 = 3/4

The multiplication rule is used to find the probability that events A and B both occur. For independent events, multiplication rule is P(A and B) = P(A) × P(B) and for dependant events, the formula is: P(A and B) = P(A) × P(B|A).

Example 2: Suppose we flip the coin three times. What is the probability of getting all three heads?

Let A be the event that we get a head on a single coin toss. The P(A) is 1/2. The P(AAA) is:

P(AAA) = P(A) × P(A) × P(A) = 1/2 × 1/2 × 1/2 = 1/8

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