 Hello and welcome to the session. Let us discuss the following question. It says, events e and f are such that probability of not e or not f is equal to 0.25. State whether e and f are mutually exclusive. Let us now move on to the solution. Now we are given that probability of not e or not f is equal to 0.25 which can also be written as probability of e dash or f dash because not e is written as e dash not f is written as f dash which is 0.25 and this is again written as probability of e dash union f dash is 0.25. Now again e dash union f dash can be written as e intersection f whole dash that is not e intersection f is equal to 0.25. This is by D Morgan's law which says that a dash union b dash is equal to a intersection b whole dash. So this is the probability of not e intersection f which is equal to 0.25. Now we know that if probability of any event a is p then probability of the event not a or we can say a dash is equal to 1 minus p. So here we are given probability of not e intersection f equal to 0.25 which is same as 1 minus probability of e intersection f which is equal to 0.25. So this implies probability of e intersection f is equal to 1 minus 0.25 which is equal to 0.75 which is not equal to 0 and we know that two events are mutually exclusive if their probability is 0. Hence the two events are not mutually exclusive. The question and the session live from now take care have a good day.