 Hello and welcome to the session. In this session we will discuss a question which says that a part determine the probability of rolling a multiple of 3 on the spinner, b part Samantha spun the spinner 90 times and got a multiple of 3, 26 times. Now first sub part is using Samantha's sample given experimental probability of obtaining a multiple of 3. Second sub part is explaining why this answer is different from the answer in part A and third sub part is does Samantha's result seems reasonable. Now before starting the solution of this question you should know a result and that is in a uniform probability model all outcomes are equally likely. Now this result will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. Now in this question a spinner with numbers 1 to 6 is given to us and here all the numbers have equal chances of being spun and from the key idea we know that in a uniform probability model all outcomes are equally likely. So in this spinner as all outcomes are equally likely that is all the numbers have equal chances of being spun so a uniform probability model. Now in the a part we have to determine the probability of rolling a multiple of 3 on this spinner. Now here the number of outcomes are 6 that is getting a number 1, 2, 3, 4, 5 and 6. So in total there are 6 outcomes. Now from these numbers we know that multiples of 3 are 3 so here number of favorable outcomes is 2 so probability p of getting a multiple of 3 on the spinner is equal to number of favorable outcomes that is 2 upon total number of outcomes that is 6 so this is equal to 1 upon 3 which is equal to 0.33 or you can say the theoretical or expected probability of getting a multiple of 3 on the spinner is equal to 0.33. Now in the b part it is given that Samantha spun the spinner 90 dice and got a multiple of 3 26 dice and in the first sub part using this sample we have to find experimental probability of obtaining a multiple of 3. So in the b part we have number of favorable outcomes is equal to 90 and here she got a multiple of 3 26 dice so experimental probability is equal to 26 upon 90 which is equal to now 2 into 13 is 26 and 2 into 45 is 90 and further on solving this gives us 0.29. So here in the a part we have got the expected probability as 0.33 and in the b part the experimental probability is 0.29. Now in the second sub part of the given question we have to explain why this answer that is the answer in the first sub part is different from the answer which we have obtained in a part. Now in the a part we have obtained the expected probability that is the probability which was expected and in the first sub part of part b we have obtained experimental probability and experimental probability is a probability which we get by actually performing the experiment. So the answer is different from part a because this is actually what we got the result after repeated number of trials and in part a the probability was expected. Now in the third sub part it is asked that does Samantha result seems reasonable? Now we have got the expected probability as 0.33 and experimental probability as 0.29. Now from here you can see that the difference between the expected probability and theoretical probability is quite small. It means if we increase the number of trials then experimental probability becomes approximately equal to expected or theoretical probability. Therefore Samantha's result is reasonable. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed the session.