 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says a pair of dice is thrown four times. If getting a doublet is considered a success, find the probability of two successes. Let us first understand Bernoulli trials and binomial distribution. Now the trials of a random experiment are called Bernoulli trials if they satisfy the following conditions. 1. There should be a finite number of trials. 2. The trials should be independent. 3. Each trial has exactly two outcomes, success or failure. 4. The probability of success remains the same in each trial. Again the probability of X successes that is probability of X equal to X where the number of successes is a random variable capital X. And this is also denoted by Px and is given by probability of X successes is equal to ncx into q raise to power n minus x into p raise to power x where x is equal to 0, 1, 2 so on till n and q is equal to 1 minus p. This Px is called the probability function of the binomial distribution. So this is a key idea behind that question. We will take the help of this key idea to solve the above question. So let's start the solution. In this question a pair of dice is thrown four times and getting a doublet is considered a success. Since dice thrown is an independent event and number of trials in the given experiment is also finite. That is it is four. The trials are for knowledge trials. Let X denote the number of doublets in an experiment of four trials. Now total number of outcomes when a pair of dice is thrown is equal to 36. Again the number of doublets when a pair of dice is thrown is equal to 6. So clearly X has the binomial distribution with n is equal to 4 and p is equal to 6 over 36 and this is equal to 1 over 6. Now according to our key idea we have probability of X successes is equal to ncx into q raise to power n minus x into p raise to power x where x is equal to 0, 1, 2 so on till n. Now here we have n is equal to 4, p is equal to 1 over 6. Now q is given by 1 minus p so this is equal to 1 minus 1 over 6 which is equal to 5 over 6. Therefore now the probability of X successes is given by x into 5 over 6 raise to power 4 minus x into 1 over 6 raise to power x. Now we have to find the probability of two successes. So probability of two successes is given by probability of x is equal to 2. So this is equal to 4c2 into 5 over 6 raise to power 4 minus 2 into 1 over 6 raise to power 2 and this is again equal to. Now 4c2 is equal to 6 into 5 over 6 into 5 over 6 into 1 over 6 into 1 over 6 and this is again equal to. 25 over 216 so the answer for that question is 25 over 216 so this completes our session. I hope the solution is clear to you. Bye and have a nice day.