probability intro

Question

A CBS News poll conducted June 10 and 11, 2006, among a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.

	better	same	worse
Republican	38	104	44
Democrat	12	87	137
none	21	90	118

Express your answers as a decimal accurate to at least 5 decimal places.

If we randomly select one of the adults who participated in this study, compute:

P(Democrat) = 

P(better) = 

P(better|Democrat) = 

P(Democrat|better) = 

P(Democrat and better) = 

Answer 1

P(Democrat)=(12+87+137)/651=236/651=0.36525

P(better) = (38+12+21)/651 = 71/651 = 0.10906

P(better I Democrat) = 12/(12+87+137) =12/236 =0.05085

P(Democrat I better) = 12/(38+12+21) = 12/71=0.16901

P(Democrat and better) = P(Democrat) x P(better I Democrat)=(236/651) x (12/236)=12/651=0.01843