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Chapter 5: Q 97. (page 331)

Lactose intolerance Lactose intolerance causes difficulty

in 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.20

(a) What percent of the entire population is lactose intolerant?

(b) What percent of people who are lactose intolerant are Asian?

Short Answer

Expert verified

Part (a) The percentage of the entire population of being lactose intolerant is 25.70%

Part (b) P(Asian|lactose)=14.01%

Step by step solution

01

Part (a) Step 1. Given Information

P(White)=82%=0.82P(Black)=14%=0.14P(Asian)=4%=0.04
02

Part (a) Step 2. Concept used

Multiplication rule: P(A鈭�B鈭�C)=P(A)脳P(B)脳P(C)

03

Part (a) Step 3. Calculation

In response to the question:

P(lactose|white)=15%=0.15P(lactose|black)=70%=0.70P(lactose|Asian)=90%=0.90

Now, for each category, calculate the likelihood of being lactose intolerant:

P(lactose鈭�white)=P(lactose|white)脳P(white)=0.15脳0.82=0.2464P(lactose鈭�black)=P(lactose|black)脳P(black)=0.70脳0.14=0.098P(lactose|鈭�Asian)=P(lactose|Asian)脳P(Asian)=0.90脳0.04=0.0360

Fill in the blanks with the corresponding probabilities:

P(lactose)=0.1230+0.0980+0.360=0.2570鈬�P(lactose)=0.2570脳100=25.70%

As a result, 25.70 percent of the population suffers from lactose intolerance.

04

Part (b) Step 1. Concept

Conditional probability: P(A|B)=P(A鈭�B)/P(A)

05

Part (b) Step 2. Calculation

P(lactose)=0.2570

Conditional probability: P(A|B)=P(A鈭�B)/P(A)

As a result, we have:

P(Asian|lactose)=P(lactose鈭�Asian)P(Asian)=0.3600.2570鈮�0.1401=14.01%

As a result, Asians account for 14.01 percent of lactose-intolerant persons.

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