Question

A CBS News poll involved 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 If we randomly select one of the adults who participated in this study, compute: (round to four decimal places) a.P(affiliated with neither party) = b.P(same) = c.P(same|affiliated with neither party) = d.P(affiliated with neither party|same) = e.P(affiliated with neither party and same) =

Answer 1

	Getting Better	About the same	Getting worse	Total
Republican	38	104	44	186
Democrat	12	87	137	236
None	21	90	118	229
Total	71	281	299	651

a) P(affiliated with neither party) = P(None) = 229/651 = 0.3518

b) P(Same) = 281/651 = 0.4316

c) P(Same and affiliated with neither party) = 90/651

P(Same | affiliated with neither party) = P(Same and affiliated with neither party)/ P(affiliated with neither party)

= (90/651)/(229/651) = 90/229

= 0.3930

d) P(affiliated with neither party|same) = P(Same and affiliated with neither party)/ P(Same)

= (90/651)/(281/651) = 90/281

= 0.3203

e) P(affiliated with neither party and same) = 90/651 = 0.1382