 Hello everyone, this is Alice Gao. This is a short video to explain the applications of the sum rule in lecture 10 from slide 16 to 18. So on slide 16, we are asked to calculate the probability that the alarm is not going and Dr. Watson is calling. This corresponds to two numbers. One, so let's see, the alarm is going is the right side of the table and then Dr. Watson is calling is the top row in the table, right? So considering both of these, we're looking at two numbers, these two numbers right here. So intuitively, all we need to do is add up these two numbers, but in mathematical terms, it looks like probability of not a and w is equal to the probability of not a and w and g plus the probability of not a and w and not g. And the two numbers are 0.036 plus 0.324, which is equal to 0.36. The second question is very similar to the first one. Conceptually the same, except we're just dealing with different numbers. So in this case, we care about the alarm is going and Mrs. Gibbons is not calling. Right? So which means we care about these two numbers. So similarly, we will add up those two numbers. Probability of a and not g is equal to the probability of a and not g and w, plus the probability of a and not g and not w, 0.048 plus 0.012. There's some is 0.06. For the third question, we want to calculate the probability that the alarm is not going. In this case, we're summing out both w and g. Right? Which means in terms of the table, we are looking at the whole right-hand side of the table and we need to add up four numbers right there. So mathematically, this looks as follows. The probability of not a is equal to the probability of not a. We're going to have to enumerate all possibilities for w and g. W and g are both true. W is true. G is false. W is false. G is true. And w, g are both false. So adding up all four numbers, 0.036 plus 0.324 plus 0.054 plus 0.486, which is 0.9. That's everything for this video. I hope by now you've mastered the application of the sum rule. Thank you for watching. I will see you in the next one. Bye for now.