Question

A survey is conducted to find out whether people in metropolitan areas obtain their news from television (Event T), an newspaper (Event N), or radio (Event R). The results show that 70% of people get news on television, 62% from newspapers, 46% from radio, 42% from television and newspapers, 26% from television and radio, 18% from newspapers and ratio, and 3% from television, newspapers and radio.

a) What is the proportion of those who obtain news from television, but not newspapers?

b) What is the proportion of those who do not obtain news from either tele- vision or radio?

c) What is the proportion of those who do not obtain news from any of these three sources?

d) Given that radio is a news source, what is the probability that a newspaper is also a news source?

e) Given that TV is a news source, what is the probability that radio is not a news source?

f) Given that newspaper is a news source, what is the probability that TV is not a news source?

Answer 1

from above P(T) =0.7 ; P(N) =0.62 ; P(R) =0.46 ; P(T n N) =0.42 ; P(T n R) =0.26 ; P(N n R) =0.18

P(T n N n R) =0.03

a)P(T n Nc) =P(T)-P(T n N) =0.7-0.42 =0.28

b)

P(T u R)^c =1-P(T u R) =1-(P(T)+P(R)-P(T n R))=1-(0.7+0.46-0.26)=0.1

c)

P(T u u R)^c =1-P(T u N u R)

=1-(P(T)+P(N)+P(R)-P(T n N)-P(T n R)-P(N n R)+P(T n N n R))

=1-(0.7+0.62+0.46-0.42-0.26-0.18+0.03)=0.05

d)

P(N|R) =P(N n R)/P(R) =0.18/0.46 =0.3913

e)

P(R^c|T) =1-P(R|T) =1-(0.26/0.7)=0.6286

f)

P(T^c |N) =1-P(T|N) =1-(0.42/0.62)=0.3226