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Baye's Theorem Calculator

Bayes’ theorem describes the probability of occurrence of an event concerning any condition. It is useful for the case of conditional probability. Bayes' formula is also known as the formula for the probability of “causes”.

What is a Baye's Theorem Calculator?

A 'Baye's Theorem Calculator' is a free online tool that helps in finding the unknown from Baye's formula. In this calculator, you can enter the given probabilities and find the unknown in Baye's formula within a few seconds.

How to Use Baye's Theorem Calculator?

Follow the steps given below to use the calculator:

Step 1: Enter the values of the given probabilities in the space provided and write the unknown as x.
Step 2: Click on "Calculate".
Step 3: Click on "Reset" to clear the field and enter the new probabilities.

How to Find a Baye's Theorem Calculator?

Conditional probability is the likelihood of the occurrence of an event, based on the knowledge of the conditions related to the event.

Bayes Formula can be given as:

P(A|B)= [P(B|A). P(A)] / P(B)

P(A) and P(B) are the respective probabilities of A and B events.

P(A|B) is the probability of event A, given that event B occurs or has occurred.

P(B|A) is the probability of event B, given that event B occurs or has occurred.

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Solved Example:

Jar-1 contains 4 white and 6 black balls while Jar-2 contains 4 white and 3 black balls. One ball is drawn randomly from one of the jars, and was found to be black. Find the probability that it was drawn from the jar-1.

Solution:

Let E₁ be the event of choosing jar-1, E₂ the event of choosing jar-2, and A be the event of drawing a black ball.

Then, P(E₁) = P(E₂) = 1/2

Also, P(A|E₁) = P(drawing a black ball from Jar-1) = 6/10 = 3/5

P(A|E₂) = P(drawing a black ball from Jar-2) = 3/7

By using Bayes’ theorem, we can know the probability of drawing a black ball from the Jar-1 out of two jars,

P(E₁/ A) = {P(E₁) × P(A / E₁)} / {P(E₁) × P(A / E₁) + P(E₂) × P(A /E₂)}

P(E₁/ A) = (3/10) / (3/10) + (3/14) = 7/12

Similarly, you can use the calculator to find the unknown from Baye's theorem:

Jar1 contains 4 white and 6 black balls while Jar-2 contains 4 white and 3 black balls. One ball is drawn randomly from one of the jars and was found to be black. Find the probability that it was drawn from the jar-1.
A man speaks the lie 2 out of 3 times. He reported that the number obtained is a five after throwing a dice. What is the probability that the number obtained is not a five?