NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.5

Consider two bags I and II. Bag I has 2 white and 3 red balls and Bag II has 4 white and 5 red balls. A ball is drawn randomly on one of the bags. We can select the probability of drawing a ball of any bag (i.e., 1/2) or a particular color (for example, white) (for example, bag I). In other words, we can find the possibility that the ball drawn is of a particular color, if we are given the bag from which the ball is drawn.

But can we find the possibility that the ball drawn is from a particular bag (for example, bag II), if the color of the ball drawn is given? Here, we have to find the inverse probability that bag II is selected when an event occurs after it is known. Eminent mathematician John Bess solved the problem of inverse probability finding using conditional probability. The formula he developed is known as the “Bayes theorem” which was published posthumously in 1763.

Bayes’ theorem is also called a formula for the possibility of “causes”. Since EI is a division of the sample space S, EI occurs and only one event EE occurs and only one can occur. Therefore, the above formula gives us the possibility of a particular EI (that is, “cause”), given that the A event has occurred. Bayes’ theorem has its applications in various situations.