I need some explanation on these 3 problems. ### Probability Problems Based on Population DataAccording to the 2018 American Community Survey, California’s population is composed of the following demographics:- 39% Latino- 37% White- 15% Asian American- 6% African American- 3% other racesAssuming people go to the mall according to these percentages, you are tasked with selecting 5 random people entering the mall for a survey.#### Questionsa) What is the probability that all 5 of them are Latino?b) What is the probability that the third person is White and the fifth one is Asian?c) What is the probability that at least one of them is an African American?

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Description: I need some explanation on these 3 problems. ### Probability Problems Based on Population DataAccording to the 2018 American Community Survey, California’s population is composed of the following demographics:- 39% Latino- 37% White- 15% Asian Americ

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A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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I need some explanation on these 3 problems.

### Probability Problems Based on Population Data

According to the 2018 American Community Survey, California’s population is composed of the following demographics:

- 39% Latino
- 37% White
- 15% Asian American
- 6% African American
- 3% other races

Assuming people go to the mall according to these percentages, you are tasked with selecting 5 random people entering the mall for a survey.

#### Questions

a) What is the probability that all 5 of them are Latino?

b) What is the probability that the third person is White and the fifth one is Asian?

c) What is the probability that at least one of them is an African American?

Expert Solution

Step 1

Since, we only answer up to 2 sub-parts, we will answer the first two. Please resubmit the question and specify the other subpart you had like answered

Define the events of going to mall of peoples from each city/region as,

L: People from Latino going to mall

W:People from White going to mall

A1:People from Asian American going to mall

A2:People from African American going to mall

O:People from other racers going to mall

From given information,

P(L)= 0.39, P(W)= 0.37, P(A1)=0.15, P(A2)=0.06 , P(O)=0.03

Suppose one experiment of selecting five peoples from mall and observing whether they are from Latino or White or Asian American or African American or other.

$S a m p l e s p a c e o f t h e e x p e r i m e n t = A l l p o s s i b l e o u t c o m e s = Ω = {L L L L L, L T L L L, L T T L L, . . . . ., W W W W W, . . . . . A 1 A 1 A 1 A 1 A 1, . . . . . A 2 A 2 A 2 A 2 A 2, . . . . . . . . O O O O O} c a r d i a l i t y o f s a m p l e s p a c e = # (Ω) = 5^{5} = 3125 L e t' ω' d e n o t e t h e t y p i c a l o u t c o m e o f t h e e x p e r i m e n t f r o m t h e a b o v e s a m p l e s p a c e . E a c h' ω' h a s u n e q u a l p r o b a b i l i t y o f o c c u r r e n c e h e r e .$

Let $X_{i} (i = 1, 2, 3, 4, 5)$ denotes number of randomly selected peoples who is entering the mall is from Latino , from white, from Asian American, from African American and from other races respectively.

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