 Hello and welcome to the session. In this session we will discuss that the conditional probability of event B given event A as the fraction of event A's outcomes that also belong to event B and interpret the answer in terms of the model. Let us see the following illustration. A family has two children. What is the conditional probability that both are boys given that at least one of them is a boy. So let us first write the sample space of the total outcomes of two children. The outcomes can be both are boys. First is boy and second is girl. First is girl and second is boy or both are girls. So the sample space is given by the set containing ordered pairs BB that is both are boys, BG first is boy and second is girl, GB first is girl and second is boy and GG both are girls where B is boy and G is girl and this is the required sample space. Now let event A be at least one of them is a boy. So favorable outcomes for event A will be given by the set containing the ordered pairs as BB, BG and GB we should note that in all these ordered pairs we have at least one boy. Also we let event B as both are boys. So favorable outcomes for event B will be given by the set containing an ordered pair that is BB as we have only one ordered pair in the sample space that contains both boys. Now favorable outcomes for both events A and B that is event A intersection B will be equal to the set containing an ordered pair given by BB. Now we have to find the probability that both are boys given that at least one is boy that is we need to find the probability of occurrence of event B given event A which is given by probability of event A intersection B upon probability of event A where probability of event A is greater than 0 and this is equal to probability of event A intersection B will be equal to probability of the set containing an ordered pair that is BB upon probability of event A and favorable outcomes for event A is given by the set. So we write probability of the set containing ordered pairs BG, GB, BB. Now we know that probability is given by number of favorable outcomes upon total number of outcomes. So here we have probability of event A intersection B and number of favorable outcomes for event A intersection B is 1 upon total number of outcomes will be given by 1, 2, 3, 4 that is 4 as we have 4 elements in the sample space. So we write 4 upon probability of event A and number of outcomes favorable to event A is 1, 2, 3. So we write 3 upon total number of outcomes that is 4. So this is equal to 1 upon 3. Now see there are three elements in event A and probability of occurrence of event B given event A is one-third of event A's outcomes and that particular outcome is the ordered pair BB which is also in event B. Similarly, conditional probability of occurrence of event A given event B will be a fraction of event B's outcomes which are also in event A. We should also note that if both events A and B have same outcomes that is set for event A is equal to set for event B then set A intersection B is also equal to set A and set B. Then we say that probability of occurrence of event B given event A will be equal to 1. This completes our session. Hope you enjoyed this session.