Explain Bayes' Theorem Used for Statistics

Bayes’ theorem describes the probability of an event based on prior knowledge of conditions that might be related to the event. If you know the conditional probability P(B|A), you can use Bayes’ rule to find out the reverse probability P(A|B).

Formula:

Demonstration

We will now understand the application of Bayes’ theorem through a demonstration:

Two bags contain red and green balls. The first bag contains two red and three green balls; the second bag contains five red and seven green balls. If a green ball is drawn from one of the bags, what is the probability that it was drawn from the first bag?

Solution: 

P(1): Probability of choosing bag 1 = 1/2

P(2): Probability of choosing bag 2 = 1/2

P(G1): Probability of getting a green ball from bag 1 = 3/5

P(G2): Probability of getting a green ball from bag 2 = 7/12

Applying Bayes’ theorem to determine the probability of a green ball being drawn from bag 1, we get: (P(1) * P(G1))/(P(1) * P(G1) + P(2) * P(G2))

= ((1/2) * (3/5))/((1/2) * (3/5)) + ((1/2) * (7/12))

= 36/71

You can learn more about conditional probability and Bayes’ theorem here.