Alrighty. So this is one of those questions where the data is really news relevant and it would be very interesting to see if you could find updated information on the same topic to see how things have changed. So despite the curiosity there, but let's focus on what they're asking us to do. The big thing for you to realize is that this is not a frequency distribution table. All right. This is a probability distribution table. That means every number in there is already a probability number. And you should be able to recognize that just by the fact that they're all less than one. All right. So, the probability is they're looking for are basically already calculated for us. Right, Okay. So all the way might, once we get to the Gibbons, we might have a little calculations. Let's see what they're asking for. The first one is asking for the probability Of the citizens that arrived were naturalised, whatever the story is in the year 2002. Right? So that's the column. The second column. And again, this is question about a single variable. This is not a joint event. So, we're going to go down to the bottom of that column for that marginal probability and just read it off the table because they've already calculated the probabilities for us. Right? So, the second question, it's a little bit more interesting, Right? This is the probability that a randomly selected person from this study did not come from El Salvador. All right. That means they want everybody else except the people from el Salvador. Right? So how are we, what's gonna be the easiest way to do it? So, again, we're talking about these marginal totals. So we can be adding up all the countries except el Salvador. I think the easiest way to calculate calculate that is just to say, well, let's start with everybody which represents 100%. And let's just subtract the probability that people that were from El Salvador. Okay, so that gets me at Mine, is that .417? Right. So I put my handy dandy calculator here Off to the size and I know you're doing the same thing. 1 -1 1 7. Right? So that .58, 3 Right, or 583. 10,000 thousands thousands. Yeah, that's the right. 1, 503,000. Let's work on our number, number skills, numeracy. All right. Next question is the probability um that the citizen is from Honduras, right? And That the citizen came in the year 2003. So now we are looking for a joint event. It's very simple. Just run along row five and column three there as marked And find that joint probability in there which is a much smaller numbers. Now we're just at 38,000 or 3.8 get that way. And finally we get to the conditional probabilities right? Which is the new skill this time around. So here we cannot do the conditional probabilities directly right? Like we did at the beginning of the lesson here, we have to use the conditional probability general formula. So this one is asking what's the um probability that the citizen is from or the person is from Guatemala Given that they came in the year 2001. Right? So remember if you can't calculate it directly, what you're doing is you're doing the joint probability divided by the givens probability. That's a key idea that the given goes on bottom Right? So joint over the given. So the joint one, we just look up off the table, we go to row four for Guatemala and 2000 a column one for 2001. And we pull off the number of 0.079. And then the probability of year one then, is that marginal probability at the bottom of the column? So that's your .3 age. What? All right. So do that division there real quick On their handy Dandy calculator and I'm getting .20 5 7 were around. I just dug it out a little bit and that's almost that's all for that. Nobody's asking me. Let's see what are they asking? The answer to be left in. It does say interpret your results in terms of percentages. We should have been doing this a long way. We'll do it at the end here. So last one there asking for is the probability Okay, it's a reverse of the last one. The probability that it came in the year 2001. Given that they came from Guatemala. Okay, I'm doing the right one there. All right. So that's gonna take the same numerator noticed because the formula is very similar. So the numerator is still the joint probability of C. One and C. Four and Y one. But the denominator is now the probability of C. Four right Given becomes the denominator. So my new monitor still pointing their 79 like it was before. But my denominator now has to go over here to Guatemala's marginal probability way out there for the total number. The total problems of people from being from Guatemala. Just 1.2 four. Run that one through Handy Dandy Calculator Real Quick. And you get point 387 for your probability for parts Or 387000s. Right. All right. So now we do need to give answers in percentages we should have all along the way. So just real quick. Right, you make a sentence that says Something like 33 0.8% or again you got to make the whole sentence. So you're gonna say something like if a person is random, if a person is selected at random from the naturalized persons in this subset, what's the best way to say that? Anyway? There's 33.8 chance that they came in the year 2002. And if a person from this study is randomly selected, There is a then going on to the next one. There's a 58.3 chance That they came from El Salvador. And if a person from this study is randomly selected, there's a 3.8 chance that they were both From Honduras and came in the year 2003. And then everybody. There's a 20 .57 chance that a person randomly selected from this study Was from Guatemala, given that they came in the year 2001. And finally, there was a 38.7 chance that a person randomly selected from this study was arrived in the year 2001, given that they were from Guatemala, all right, steven type of all those sentences, and that's all for this problem.