 So, today we're going to discuss some probability and we're going to talk about conditional probability using a two-way table. So the table, it's on the next slide, I'll show it in a second, shows the number of survey subjects who have received and not received a speeding ticket in the last year and the color of their car. We want to find the probability that a randomly chosen person A has a speeding ticket given they have a red car and B has a red car given that they have a speeding ticket. So we're going to look at the data now. So this column represents speeding tickets. So there's 15 red cars who have received speeding tickets, 45 non-red cars that have received speeding tickets and then 45 plus 15 would be 60. There's 60 cars total that have received speeding tickets. Then we have 135 cars that are red that did not speed, did not get a ticket when they sped 470 that have not been ticketed that are not red and then 470 plus 135 gives you the 605. Then you can look at this row for red cars 15 plus 135 gives us the 150 and then this row for non-red cars 45 plus 470 equals 515. Then this two-way table we went ahead and did 60 plus 605 to get the total number of cars surveyed and you could also get to the 665 by doing 150 plus 115. So the first question here, we're looking at cars that have a speeding ticket given that they are red. So for red cars we're going to look at this row right here. There are 150 total cars, total red cars, see red and red, okay, 150 total red cars of which 15 had speeding tickets. And if I wanted to write this out with probability notation, I would say we're looking for the probability that a car has been ticketed given, we draw a line to represent given, it is red. So the probability that a car is ticketed given that it's red is 15 over 150 which would reduce to 1 over 10 or 0.1. Moving along to part B, part B says the probability that a car is red given that it has a speeding ticket. So we're going to look at the cars that have been ticketed. There are 60 cars total that were issued a ticket of those 60 cars, 15 of them were red. If I wanted to write this out with probability notation, I would say the probability that a car is red given it was issued a ticket, 15 over 60 would reduce to 1 over 4 which would reduce to 0.2.