 Hello everyone this is Alice Gao. In this video I'm going to show you two applications of the product rule and this is regarding the two clicker questions in lecture 10 on slides 20 and 21. On slide 20 we want to calculate the probability that Dr. Watson is calling given that the alarm is not going. So the probability of w given not a, based on our product rule formula this is equal to the joint probability of w and not a divided by the probability of not a. Normally we would have to go back to the joint distribution to calculate both the numerator and the denominator, but luckily for us or because of my awesome design of the clicker questions I already asked you to calculate both quantities in the previous slides. So you can use them directly. This is equal to 0.36 divided by 0.9 which is 0.4. The second question on slide 21 is very similar. We want to calculate the probability that Mrs. Gibbons is not calling given that the alarm is going. So the probability of not g given a, this is equal to the probability of not g and a divided by the probability of a. So do we have both of these information? Well we certainly already have the joint probability over a and not g. So we have that, but we don't directly have the probability of a. That's okay. That's pretty easy to get right because we have the probability of not a. So the probability of a is just one minus the probability of not a which is 0.1. So let's plug in this is equal to 0.06 divided by one minus 0.1. So 0.06 divided by 0.1 which is 0.6. So option C. That's it for this video. After watching this video you should be able to calculate the conditional probability using the product rule. Thank you for watching. I will see you in the next video. Bye for now.