 Hi friends, I am Purva and today we will work out the following question. An instructor has a question bank consisting of 300 easy true or false questions, 200 difficult true or false questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question. Now we have to find the probability that the question is easy given that it is a multiple choice question. Now we can clearly see that it is a problem of conditional probability. So let E and F be two events associated with the sample space of a random experiment. Then the conditional probability of the event E given that F has occurred, that is probability of E given F is given by probability of E given F is equal to probability of E intersection F upon probability of F and here probability of F is not equal to zero. So this is the key idea behind our question. Let us begin with the solution now. Now we are given that there are 300 easy true or false questions, 200 difficult true or false questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. So the total number of questions will be 300 plus 200 plus 500 plus 400. So in the sample space for this experiment, there will be total of 300 plus 200 plus 500 plus 400. That is this is equal to 1400 questions. Now we have to find the probability that it will be an easy question given that it is a multiple choice question. So let E be the event that it is an easy question and let F be the event that it is a multiple choice question. Now E is the event that it is an easy question. So E will have 300 easy true or false questions and 500 easy multiple choice questions. So we have E will have 300 easy true or false questions plus 500 easy multiple choice questions and this is equal to total of 800 questions. So we have 800 easy questions and F is the event that it is a multiple choice question. Now F will have 500 easy multiple choice questions and 400 difficult multiple choice questions. So F will have 500 easy multiple choice questions plus 400 difficult multiple choice questions. So in all F will have 900 multiple choice questions. So we have probability of F is equal to 900 upon 1400 because there are 1400 total number of questions and out of which 900 are multiple choice questions and this is equal to 9 upon 14. Now E is the event that the question is easy and F is the event that it is a multiple choice question so E intersection F will be the event that the questions are easy and multiple choice both. So E intersection F is the event that questions are easy and multiple choice. Now there are only 500 easy multiple choice questions so we get E intersection F is equal to 500 easy multiple choice questions so probability of E intersection F is equal to 500 upon 1400 and this is equal to 5 upon 14. Now in this question we have to find the probability that it will be an easy question given that it is a multiple choice question so we have to find probability of E given F. Now by key idea we know that probability of E given F is equal to probability of E intersection F upon probability of F. So applying the formula. Probability of E given F is equal to probability of E intersection F upon probability of F we get this is equal to probability of E intersection F is equal to 5 upon 14 divided by probability of f is equal to 9 upon 14. And this is equal to 5 upon 9. So we have got our answer as 5 upon 9. Hope you have understood the solution. Bye and take care.