3 the census bureau reports that 27 of california residents...

3. The Census Bureau reports that 27% of California residents are foreign-born. Suppose that you choose 3 Californians independent of each other at random. There are eight possible arrangements of foreign (F) and domestic (D) birth. For example, FFD means the first two are foreign-born and the third is not. Order matters! A. Write down all eight arrangements: B. Calculate the probability of each arrangement in part a. C. Let the random variable X be the number of foreign-born people in each group of three. What are the possible values of X? D. Make a probability distribution table for X (use the work you completed in parts a-c to help make the table) E. What is the expected number of foreign-born residents in a randomly selected group of three?

Transcript

00:01 In this problem, we're going to use a tree diagram to help us solve all the parts.

00:07 And it says that you're going to choose three californians independent of each other at random.

00:14 So the first person we pick might be foreign -born or domestic.

00:23 The second person we select might be foreign -born or domestic.

00:30 And the third person we select might be foreign -born or domestic.

00:44 And part a says write down all eight arrangements.

00:50 So part a, to get to the bottom here, we would follow path fff.

00:59 To get to the bottom here, we would follow the path ffd.

01:04 To get to the bottom here, we'd follow the path ffd.

01:08 Fdf to get here.

01:12 We'd follow the path f, d, d to get here.

01:18 We would follow the path d, f, f, f.

01:23 Here would be d, f, d.

01:27 Here would be d, d, d, f, and finally, d, d, d.

01:37 D.

01:39 D.

01:40 Is to calculate the probability of each arrangement.

01:48 So this will be part b, it's the probability of each arrangement.

01:56 So for the probability of fff, it told us that the census bureau reports that 27 % of california residents are foreign -born.

02:09 So the probability of an f is 0 .27, so that means that the remaining percentage would be domestic.

02:23 So therefore, there has to be 73 % that are domestic.

02:29 This way when you add those up, you get a 1.

02:34 So now if we go back to our chart, then the probability of the first person being foreign born is 0 .27.

02:43 The probability of the second person being born born, is 0 .27, and the probability of the third person being foreign born is 0 .27.

02:55 So we have an o of 0 .0 .0 .09 -683.

03:07 For the second one, the probability of the person being foreign born, two times in a row, and then a domestic, we would have 0 .27 for foreign borns, and 0 .73 is a probability for domestic, and if we multiply those three together, we get 0 .053 -217.

03:35 The next one, for 4 -n -born, it's 0 .27.

03:39 For domestic, it's 0 .73, and for born -born, it's 0 .27, which gets us the same probability as up above.

03:51 For the next one, the probability of 4 -and -born is 0 .27.

03:56 Domestic is 0 .73 and domestic is 0 .73.

04:02 And if we multiply those out, we will get a 0 .143883.

04:11 The next scenario is domestic, followed by 2 foreign -born.

04:25 And that will be 0 .053 -217.

04:31 Next, we have domestic, followed by foreign -born, followed by domestic...