Question

9.98. Consider the data of Exercise 9.92. Suppose a person from the continental united states does not have broadband access from home. What is the probability that the person lives in the southeast?

Exercise 9.92. The population of the continental united states is distributed as follows: 40% in the north east, 10% in northwest, 30% in the southwest, and 20% in the southeast. The population with broadband access from home is distributed as follows: 85% in the northeast have access, 90% in the northwest have access, 95% in the southwest have access, and 75% in the southeast have access. If we pick one person at random from the continental US, what is the probability that he has broadband access from home?

Answer 1

1)

probability that he has broadband access from home

=P(north east and has broadband access from home)+P(northwest and has broadband access from home)+P(southwest and has broadband access from home)+P( southeast and has broadband access from home)=0.4*0.85+0.1*0.9+0.3*0.95+0.2*0.75=0.865

2)

P(not have broadband access)=1-P(have broadband access)=1-0.865=0.135

hence  probability that the person lives in the southeast given not have  broadband access)

=P( southeast and not have broadband access)/P(not have broadband access)

=0.2*(1-0.75)/0.135=0.3704