 Hi and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says, A speaks the truth, 8 out of 10 times the die is tossed he reports that it was 5. What is the probability that it was actually 5? Let us see the solution to this question. First of all, let E1, E2 and A be the events defined as follows. Let E1 be the event that 5 occurs and let E2 be the event that 5 does not occur. Let A be the event that man reports that it is 5. So we see that probability of the event that 5 occurs is 1 by 6 and probability of the event E2 that is 5 does not occur is 5 by 6. Now probability A oblique E1 is the probability 8 upon 10 that is equal to 4 by 5 and probability A upon E2 is the probability that the man does not 1 minus 4 by 5 and that is equal to 1 by 5. Now we have to find probability E1 upon A that is when A is given that is the probability that on the die so we have probability E1 when A is given is equal to probability E1 into probability A upon E1 divided by probability E1 into probability A upon E1 plus probability of E2 into probability A upon E2 that is equal to 1 by 6 into 4 by 5 divided by 1 by 6 into 4 by 5 plus 5 by 6 into 1 by 5 and that is equal to 4 by 9 which is also our answer to this question. So I hope that you understood the solution and enjoyed the session. Have a good day.