Question

The World Health Organization (WHO) keeps track of how many incidents of leprosy there are in the world. Using the WHO regions and the World Banks income groups, onc can sask if an income level and a WHO region are dependent on each other in terms of predicting where the disease is. Data on leprosy cases in different countries was collected for hte year 2011 and a summary is present in the following table.

1. Two-Way Table of Leprosy Cases:

WHO Region:	World Bank Income Group:				Row Total
	High Income	Upper Middle Income	Lower Middle Income	Low Income
Americas	174	36028	615	0	36817
Eastern Mediterranean	54	6	1883	604	2547
Europe	10	0	0	0	10
Western Pacific	26	216	3689	1155	5086
Africa	0	39	1986	15928	17953
South-East Asia	0	0	149896	10236	160132
Column Total	264	36289	158069	27923	222545

1. Compute the probability that a person with leprosy is from the Americas. Show your work below:
2. Compute the probability that a person with leprosy lives from a high-income country. Show your work below:
3. Compute the probability that a person with leprosy is from the Americas and a high-income country. Show your work below:
4. Compute the probability that a person with leprosy is from a high-income country, given they are from the Americas. Show your work below:
5. Compute the probability that a person with leprosy is from a low-income country. Show your work below:
6. Compute the probability that a person with leprosy is from Africa. Show your work below:
7. Compute the probability that a person with leprosy is from Africa and a low-income country. Show your work below:
8. Compute the probability that a person with leprosy is from Africa, given they are from a low-income country. Show your work below:
9. Are the events that a person with leprosy is from Africa and Low-income country independent events? Why or why not? Explain below:
10. Are the events that a person with leprosy is from the Americas and high-income country independent events? Why or why not? Explain below:

Answer 1

(a)

P( a person with leprosy is from the Americas ) = 36817/ 222545 = 0.1654

(b)

P( a person with leprosy lives from a high-income country. ) = 264/222545 = 0.0012

(c)

P( a person with leprosy is from the Americas and a high-income country. ) = 174/ 222545 = 0.0007818

(d)
P( a person with leprosy is from a high-income country, given they are from the Americas. ) = P( a person with leprosy is from a high-income country AND they are from the Americas. )/ P(they are from the Americas)

= 174/36817

= 0.004726

(e)
P( a person with leprosy is from a low-income country. ) = 27923/ 222545 = 0.1255

(f)
P( a person with leprosy is from Africa. ) = 17953/ 222545 = 0.0807

(g)

P( a person with leprosy is from Africa and a low-income country. ) = 15928/ 222545 = 0.0716

(h)

P( a person with leprosy is from Africa, given they are from a low-income country. ) = P( a person with leprosy is from Africa, AND they are from a low-income country. )/ P(they are from a low-income country)

= 15928/ 27923

= 0.5704

(i)

P( a person with leprosy is from Africa ) = 17953/222545 = 0.0807

P( Low-income country ) = 27923/ 222545 = 0.1255

So,

P( a person with leprosy is from Africa ) X P( Low-income country ) = 0.0807 X 0.1255 = 0.0101

But,

P( a person with leprosy is from Africa AND Low-income country ) = 15928/ 222545 = 0.0716

Since P( a person with leprosy is from Africa ) X P( Low-income country ) = 0.0101 P( a person with leprosy is from Africa AND Low-income country ) = 0.0716, the events that a person with leprosy is from Africa and Low-income country are not independent events.

(j)

P( a person with leprosy is from the Americas ) = 36817/222545 = 0.1654

P( high-income country ) = 264/222545 = 0.001186

So,

P( a person with leprosy is from the Americas ) X P( high-income country ) = 0.0001962

But,

P( a person with leprosy is from the Americas AND high-income country ) = 174/222545 = 0.0007818

Since P( a person with leprosy is from the Americas ) X P( high-income country ) = 0.0001962 P( a person with leprosy is from the Americas AND high-income country ) = 0.0007818, the events that a person with leprosy is from the Americas and high-income country are not independent events.