Question

in a sample of 150 residents, each person was asked if he or she favored the concept of having! 9-3 \p a single countrywide police agency. The residence (city or outside the city) and the responses 4 of the residents are summarized in the following table. Oppose (A) 40 Favor (F) Residence City 80 10 20 Outside of City (OC) If one of these residents was to be selected at random, what is the probability that the person will (a) favor the concept given that the person selected is a city residenr? (b) favor the concept given that the person selected is a resident from outside the city? c) favor the concept or the person selected is a city resident d) favor the concept or the person selected is a resident from outside the city

Answer 1

	Favor	Oppose	Total
In City	80	40	120
Outside City	20	10	30
Total	100	50	150

Let A be the event that the person favors the concept    
Let B be the event that the person is a city resident    
     
     
a) To find P(A given B)    
   = P(A | B)    
     
P(A AND B) P(B) 80 150 120 150 80 120

   = 0.6667    
P(person favors the concept given he is a city resident) = 0.6667    
     
b) To find P(A given B')    
   = P(A | B')    
   
PCA AND B') P(B') 20 一30 150 20 30

   = 0.6667    
P(person favors the concept given he is an outside city resident) = 0.6667    
     
c) To find P(A or B)    
P(A or B) = P(A) + P(B) - P(A AND B)    
  
100 120 80 150 150 150 140 150

     
   = 0.9333   
     
     
d) To find P(A or B')    
P(A or B') = P(A) + P(B') - P(A AND B')    
  
100 30 20 150 150 150 110 150

   = 0.7333