Question

Investment advisors might subscribe to the Business Times (BT) or Straits Times (ST). For those investment advisors who subscribe to at least one of the papers, one-third subscribe to only one newspaper, ST, and one-fourth subscribe to only one newspaper, BT. 40% of the investment advisors subscribe to both papers. (a) Complete the probability table below (the grey boxes).

BT BTC TOTAL

ST

STC

TOTAL 1

Total 1.0 (b) Suppose an investment advisor receives at least one of the papers. What is the probability they receive the BT?

Answer 1

a) 1/3 rd to only ST  that is 0.3333 to only ST  
1/4 th to only BT  that is 0.25 to only BT  
0.4 to both papers  0.4 to both papers  
     
0.3333 is ST , which is ST-BTC cell    
0.25 is BT , which is BT-STC cell    
BT-ST cell is 0.4    
Total probaility = 1    
Using, above we fill the remaining cells of the table    
Hence, the probability table is     

	BT	BTC	Total
ST	0.4	0.3333	0.7333
STC	0.25	0.0167	0.2667
Total	0.65	0.35	1

b) Let B: event that the investment advisor receives BT      
Let A : event that the investment advisor receives atleast 1 paper      
To find P(B | A)      

                       

                     = 0.661     
       
P(investor advisor receives BT given he receives atleast one paper) = 0.661