[Video] Q21: The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. group x consisted of 100 people who observed early bedtimes, and group y consisted of 100 people who observed later bedtimes. if a person is chosen at random from those who recalled at least 1 dream, what is the probability that the person belonged to group y ?

Explanation for Question 21 From the Math (Calc) Section on the Official Sat Practice Test 1

So 21 shows this a table with a lot of information, 2 right? And they tell us a group asks, consisted of a hundred people who 3 observed early bedtimes. Right? So the total on group X was a hundred and 4 the group Y so we're right there. 5 Um, this is people that we serve later bedtime. 6 So they also tell us what these two are. Right? 7 So group X was people who observed early bedtimes. 8 So here we have early and here we have late, 9 and then dreams were called during the week, 10 right? So this is how many dreams that they could remember. 11 And the question asks us if a person is chosen at random, 12 from those who were called at least one dream. 13 So we're not choosing from everybody to start with, 14 right? We're only choosing from the people who recalled one dream chosen 15 at random, from those who were called at least one dream. 16 So we're only picking from this one, right? Because everyone in those two columns 17 recalled at least one dream or more. 18 Now the total here, the total number of those people would be the 39 19 plus the 1 25. So if we take that, 20 we plug it in our calculator, 39 plus 1 25, 21 we get 164. So we're choosing out of 164 people here 22 is asking what is the probability that the person belonged to group Y? 23 Right? So now we just need to see how many people in our nice 24 little box here belong to group Y. And that's going to be these two 25 boxes because these two boxes are in line with the group Y row. 26 So that's 11 plus 68. And when we put 11 plus 68 in our 27 calculator, we get 79. Right? 28 So our answer is going to be group wide over one or more dreams, 29 which shows us our correct answer has to be see.