Question

a survey on ownership of satellite TV system shows the following data:

A survey on ownership of satellite TV systems shows the following data: Region East Midwest Southwest West Total Currently Own 25 12 197 41 Likely to Purchase 129 87 38 105 Neither 536 421 86 302 Total Complete the table and answer the following: (Write answers either as fractions or as decimals to 4 decimal places.) a) What is the probability that someone is likely to purchase a satellite system? b) What is the probability that someone owns a system and lives in the southwest? c) Given a person lives in the west, what is the probability that they are likely to purchase a satellite system? d) Given that someone is likely to purchase a system what is the probability that they live in the east?

Answer 1

	East	Midwest	Southwest	West	Total
Currently Own	25	12	197	41	275
Likely to Purchase	129	87	38	105	359
Neither	536	421	86	302	1345
Total	690	520	321	448	1979

a.) The probability that someone is likely to purchase a satellite system =   

350 1979 0.1814

b.) The probability that someone owns a system and lives in the southwest = $\frac{197}{1979} = 0.0995$

c.) The probability that a person likely to purchase a satellite system, given that he or she lives in the west = $\frac{\frac{105}{1979}}{\frac{448}{1979}}= \frac{105}{448}=0.234$

d.) The probability that someone lives in the east, given that he or she is likely to purchase a system = $\frac{\frac{129}{1979}}{\frac{359}{1979}}= \frac{129}{359}= 0.359$