Lactose intolerance causes difficulty digesting dairy products that contain lactose (milk sugar). It is particularly commonamong people of African and Asian ancestry. In the United States (ignoring other groups and people who consider themselvesto belong to more than one race), 82% of the population is white, 14% is black, and 4% is Asian. Moreover, 15% of whites,70% of blacks, and 90% of Asians are lactose intolerant.(a) What percent of the entire population is lactose intolerant? (Enter your answer rounded to one decimal place.)percent of the population who are lactose intolerant :0.3(b) What percent of people who are lactose intolerant are Asian? (Enter your answer rounded to two decimal places.)percent of people who are lactose intolerant are Asian =0.1

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Asked Dec 13, 2019
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Lactose intolerance causes difficulty digesting dairy products that contain lactose (milk sugar). It is particularly common
among people of African and Asian ancestry. In the United States (ignoring other groups and people who consider themselves
to belong to more than one race), 82% of the population is white, 14% is black, and 4% is Asian. Moreover, 15% of whites,
70% of blacks, and 90% of Asians are lactose intolerant.
(a) What percent of the entire population is lactose intolerant? (Enter your answer rounded to one decimal place.)
percent of the population who are lactose intolerant :
0.3
(b) What percent of people who are lactose intolerant are Asian? (Enter your answer rounded to two decimal places.)
percent of people who are lactose intolerant are Asian =
0.1
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Lactose intolerance causes difficulty digesting dairy products that contain lactose (milk sugar). It is particularly common among people of African and Asian ancestry. In the United States (ignoring other groups and people who consider themselves to belong to more than one race), 82% of the population is white, 14% is black, and 4% is Asian. Moreover, 15% of whites, 70% of blacks, and 90% of Asians are lactose intolerant. (a) What percent of the entire population is lactose intolerant? (Enter your answer rounded to one decimal place.) percent of the population who are lactose intolerant : 0.3 (b) What percent of people who are lactose intolerant are Asian? (Enter your answer rounded to two decimal places.) percent of people who are lactose intolerant are Asian = 0.1

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Expert Answer

Step 1

(a)

Let us define the events:

 

W:White

B:Black

A:Asian

L:Lactose intolerant.

 

From the given information,

 

The percent of white population is 82%. That is, P(W)=0.82.

The percent of black population is 14%. That is, P(B)=0.14.

The percent of Asian population is 4%. That is, P(A)=0.04.

The percent of whites are lactose intolerant is 15%. That is, P(L|W)=0.15.

The percent of blacks are lactose intolerant is 70%. That is, P(L|B)=0.70.

The percent of Asians are lactose intolerant is 90%. That is, P(L|A)=0.90.

Step 2

The percentage of the entire population is lactose intolerant is ...

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P(Lactose intolerant) = P(L\W)P(W)+P(L|B)P(B)+P(L|4)P(A) = (0.15x0.82)+ (0.70×0.14)+(0.90×0.04) = 0.257 %3D = 25.7%

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