 Hello and welcome to the session. Let us discuss the following question. It says if e and f are events such that probability of e is 1 by 4, probability of f is 1 by 2 and probability of e and f is 1 by 8, find probability of e or f, probability of not e and not f. Before moving on to the solution we need to know some basic facts. These are probability of a or b or we can say probability of a union b is probability of a plus probability of b minus probability of a and b or we can say probability of a intersection b. And probability of event a is p then probability of the event not a is 1 minus p. We also need to know the B Morgan's law which is not a which is denoted by a dash intersection not b that is b dash. A union b is equal to a union b whole dash that is not a and not b is equal to neither a nor b that is a union b whole complement that is not a union b. So this knowledge will work as key idea. Let us now move on to the solution. We are given that probability of e is 1 by 4, probability of f is 1 by 2 and probability of e and f is 1 by 8. So we have to find probability of e or f that is probability of e union f which is equal to probability of e plus probability of f minus probability of e and f. Now probability of e is 1 by 4 probability of f is 1 by 2 probability of e and f that is probability of e intersection f is 1 by 8. Solving this is equal to 5 by 8. So the probability of e or f is 5 by 8. Now in the second part we have to find probability of not e and not f not e is denoted by e dash and not f is denoted by f dash. So we have to find probability of e dash and f dash which can also be written as probability of e dash intersection f dash. Now as we discussed in the key idea a dash intersection b dash is written as a union b dash by the D Morgan's law. So this is equal to probability of e union f whole dash. And we know that probability of not a is 1 minus b if probability of a a a is b. So here probability of e union f whole dash is same as probability of not e union f which is equal to 1 minus probability of e union f which is same as 1 minus probability of e or f. Now probability of e or f is 5 by 8. So this is 1 minus 5 by 8 which is equal to 3 by 8. Hence probability of e or f is 5 by 8 and probability of not e and not f is 3 by 8. And this completes the question.