 Hello and welcome to the session I am Deepika here. Let's discuss a question which says in a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is 10 inverse 1 over 2 raised to power 5, 9 over 10 raised to power 5, 9 over 10. That is we have to choose the correct option from A, B, C and D. So let's start the solution. Now here we are given a box containing 100 bulbs, 10 are defective. We have to find the probability that out of a sample of 5 bulbs none is defective. Now we know that trials of a random experiment are called Bernoulli trials. If they are finite in number, the trials are independent and each trial has exactly two outcomes, success or failure and the probability of success remains the same in each trial. Now here event of selecting bulbs is independent also the number of trials is finite that is 5. So the trials of the above experiment are Bernoulli trials. Let X denote the number of defective bulbs in a sample of 5 bulbs as the binomial distribution with n is equal to 5 and p is equal to 10 over 100 which is equal to 1 over 10 because we are given a box containing 100 bulbs in which 10 are defective that is probability of success is 1 over 10 where success is that the bulb is defective. Therefore q which is equal to 1 minus p is equal to 1 minus 1 over 10 and this is equal to 9 over 10. Probability of X success is equal to n c x 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. Now we have to find the probability that out of a sample of 5 bulbs none is defective that is we have to find the probability of X is equal to 0. So this is equal to 5 c 0 into 9 over 10 raise to power 5 minus 0 into 1 over 10 raise to power 0 because we have n is equal to 5 p is equal to 1 over 10 and q is equal to 9 over 10. So probability of 0 success is equal to 5 c 0 into 9 over 10 raise to power 5 minus 0 into 1 over 10 raise to power 0 and this is equal to 1 into 9 over 10 raise to power 5 into 1 because 5 c 0 is 1 and 1 over 10 raise to power 0 is also 1. So probability of X is equal to 0 is equal to 9 over 10 raise to power 5 but this is our option c. Hence c is the correct option. 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.