 Hello and welcome to the session. In this session we discuss the following question which says In a simultaneous throw of a pair of dice, find the probability of getting First, a sum greater than 9 Second, a doublet of odd numbers Consider E to be an event. Now the formula for finding the probability of Occurrence of an event E is given by P E and this is equal to Number of outcomes favorable to the event E upon total number of possible outcomes This is the key idea to be used in this question Now let's see the solution. In the question we have that a pair of dice are thrown simultaneously We have to find the probability of getting a sum greater than 9 and a doublet of odd numbers First of all let's see what would be the possible outcomes when we throw a pair of dice So these are the possible outcomes when two dice or a pair of dice are thrown simultaneously So as you can see total number of possible outcomes is equal to 36 Now let's solve the first part of the question in which we have to find the probability of getting a sum greater than 9 So consider let even be an event of getting a sum of two numbers greater than 9 So we have to find the probability of even by the probability of getting a sum of two numbers greater than 9 These are the total outcomes when we throw a pair of dice simultaneously of these We have to find the outcomes when the sum of two numbers is greater than 9 So we find that 4, 6, then 5, 5, 5, 6, 6, 4, 6, 5 and 6, 6 are the six outcomes in which the sum of the two numbers is greater than 9 Like if you consider 4, 6, the sum of two numbers is equal to 4 plus 6 that is equal to 10 which is obviously greater than 9 Then we have 5, 5, the sum of two numbers is 10 that is greater than 9 5, 6, sum of two numbers is 11 which is obviously greater than 9 Then 6, 4, sum of two numbers is 10 which is greater than 9 Then 6, 5, sum of two numbers here is 11 which is greater than 9 Then 6, 6, sum of two numbers is 12 which is greater than 9 So we find the number of outcomes favourable to event even is equal to 6 And the favourable outcomes are 4, 6, 5, 5, 6, 5 So now probability of even that is probability of getting a sum greater than 9 is equal to The number of outcomes favourable to even which is equal to 6 upon the total number of possible outcomes which is 36 So we get 6 upon 36 Now 6, 6 times 36 so this is equal to 1 upon 6 So we say probability of the event even that is the probability of getting a sum greater than 9 is equal to 1 upon 6 Now the next part of the question says find the probability of getting a doublet of odd numbers For this case also the total number of possible outcomes is 36 Now first of all we consider let E2 be the event of getting a doublet of odd numbers And we have to find the probability of E2 First of all let's see how many doublets do we have in this case when two dice are thrown simultaneously So as you can see we have 6 doublets Now since we need to find the probability of getting a doublet of odd numbers So out of these 6 doublets let's see what are the doublets of odd numbers Now this 1, 1 is the doublet of odd numbers 3, 3 is the doublet of odd numbers 5, 5 is the doublet of odd numbers So we say the favourable outcomes are 1, 1, 3, 3, 5, 5 That is number of outcomes favourable to even E2 is equal to 3 So now probability of E2 that is probability of getting a doublet of odd numbers is equal to the number of outcomes favourable to E2 that is 3 upon the total number of possible outcomes which is 36 So probability of E2 is equal to 3 upon 36 Now 3, 12 times is 36 so this is equal to 1 upon 12 So we get probability of E2 is equal to 1 upon 12 So our final answer is for the first part we have 1 upon 6 and for the second part our answer is 1 upon 12 So this completes the session hope you have understood the solution of this question