 Hi and welcome to the session. Let us discuss the following question. Question says, a dice is thrown twice. What is probability that 5 will not come up either time? Second part is, 5 will come up at least once. Let us now start with the solution. Now we know a dice is thrown twice. So total number of outcomes possible are shown here. This number shows outcome of the first throw and this number shows outcome of the second throw. So when dice is thrown twice, total number of possible outcomes is equal to 6 multiplied by 6. That is 36. Now in the first part of the given question we have to find the probability that 5 will not come up either time. Now clearly we can see in this column and in this row, 5 is coming at least once. So total number of outcomes in which 5 will not come up either time are 36 minus 11. Clearly we can see here number of outcomes is 6 and in this row number of outcomes is 6. Now this outcome is common in this row and in this column. So we get total number of outcomes where 5 will come at least once is equal to 11. So we can write total number of outcomes where 5 will come at least once is equal to 11. So we get total number of outcomes where 5 will not come up either time are 36 minus 11 that is 25. Now probability that 5 will not come up either time is equal to number of favorable outcomes to 5 not coming up either time upon total number of possible outcomes. Now we know number of favorable outcomes to 5 not coming up either time is equal to 25 and total number of possible outcomes is equal to 36. So we get probability that 5 will not come up either time is equal to 25 upon 36. Now this completes the first part of the given question. Now let us start with the second part. Now we have to find probability that 5 will come up at least once. Now we know total number of outcomes where 5 will come at least once is equal to 11. So we can write total number of outcomes favorable to 5 at least once is equal to 11. Now we know probability that 5 will come up at least once is equal to number of outcomes favorable to 5 at least once upon total number of possible outcomes. Now we know number of outcomes favorable to 5 at least once is equal to 11 and total number of possible outcomes is equal to 36. So probability that 5 will come up at least once is equal to 11 upon 36. Now required answer for the first part is equal to 25 upon 36 and for second part is 11 upon 36. This is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.