 Hello and welcome to the session. In this session we discussed the following question which says, a machine is composed of three parts. The probability that each of these parts function properly is 0.92, 0.76 and 0.85. The machine functions only if all the parts function together. Find the probability that the machine will fail. Let's proceed with the solution now. We consider let E1 be the event that the part 1 of the machine functions and we take E2 to be the event that the part 2 of the machine functions also E3 be the event that the part 3 of the machine functions. We take probability of event that is the part 1 of the machine functions be equal to 0.92 then probability of E2 that is the probability that the part 2 of the machine functions be equal to 0.76 and probability of E3 which is the probability of the part 3 of the machine functions be equal to 0.85. In the question it's given that the machine functions only if all the parts function together. So the probability that the machine functions is equal to the probability of even and E2 and E3. That is all the three parts of the machine function together and this is equal to probability of even intersection E2 and this would be equal to probability of even multiplied by probability of E2 multiplied by probability of E3 which is further equal to 0.92 multiplied by 0.76 multiplied by 0.85. And so this is equal to 0.594 that is the probability that the machine functions is equal to 0.594. We have to find the probability that the machine will fail. So the probability that the machine fails would be equal to 1 minus the probability that the machine functions. So this is equal to 1 minus 0.594 which is equal to 0.406 which is the probability that the machine fails. So this is our final answer. This completes the session. Hope you have understood the solution of this question.