 Hello, I am welcome to the session, I am Deepika here. Let's discuss the question which says, on a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing? Now, we know that the probability of x successes is equal to mcx into q raise to power n minus x into p raise to power x, where x is from 0 to n and q is equal to 1 minus p. So, this is a key idea. For the above question, we will take the help of this key idea to solve the above question. So, let's start the solution. In this question, there is a multiple choice examination with three possible answers for each of the five questions. So, selecting one answer from three possible answers in each question is independent of each other. That is, the trials of the given experiment, independent, again the number of trials is finite, that is five. So, the trials of the given experiment are independent and finite. Hence, the trials are, that is the trials of the given experiment are the nonlit trials. Now, we have to find the probability that a candidate would get four or more correct answers just by guessing. Let x denote the number of correct answers. So, clearly x has the binomial distribution with n is equal to five and p, which is the probability of success. Now, probability of success here is one over three. So, p is equal to one over three. Now, we know that q is equal to one minus p. So, this is equal to one minus one over three, which is equal to two over three. Now, according to our key idea, we have probability of x successes is equal to mcx into q raise to power n minus x into p raise to power x, where x is from zero to n and q is equal to one minus p. Now, here we have n is equal to five, p is equal to one over three and q is equal to two over three. Therefore, we have probability of x successes is equal to five cx into two over three raise to power five minus x into one over three raise to power x. Now, we have to find the probability of four or more successes. So, this is equal to probability of x is equal to four and five, because x can take value from zero to n and here n is five. So, we want to find the probability of four or more successes, that is we want to find the probability of x is equal to four and five. So, this is equal to probability of four successes, that is probability of four correct answers plus probability of five correct answers, that is probability of five successes and this is again equal to five c four into two over three raise to power five minus four into one over three raise to power four plus five c five into two over three raise to power five minus five into one over three raise to power five. Now, this is equal to five because five c four is five into two over three into one over eighty one plus now five c five is one into two over three raise to power zero, which is also one into one over three raise to power five which is one over two forty three. So, this is equal to ten over two forty three plus one over two forty three and this is again equal to eleven over two forty three. Hence, the probability that a candidate would get four or more correct answers just by guessing is eleven over two forty three. So, this is the answer for the above question. This completes our session. I hope the solution is clear to you. Bye and have a nice day.