Question 1210434
.
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.

<pre>
           better same worse
Republican   38    104   44
Democrat     12     87  137
none         21     90  118
</pre>Express your answers as a decimal and round to the nearest 0.001 (in other words, type 0.123, not 12.3% or 0.123456).
If we randomly select one of the adults who participated in this study, compute:
a. P(Democrat) =
b. P(better) =
c. P(better | Democrat) =
d. P(Democrat | better) =
e. P(Democrat and better) =
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
(a)  P(Democrat) = {{{(12+87+137)/651}}} = 0.363  (rounded).

     The sum of numbers in the row "Democrat" is related to the total.



(b)  P(better) = {{{(38+12+21)/651}}} = 0.109  (rounded).

     The sum of numbers in column "better" is related to the total.



(c)  P(better | Democrat) = {{{12/(12+87+137)}}} = 0.051  (rounded).

     The number in the intersection of column "better" with the row "Democrat"
     is related to the total in the row "Democrat"



(d)  P(Democrat | better) = {{{12/(38 + 12 + 21)}}} = 0.169  (rounded).



(e)  P(democrat and better) = {{{12/651}}} = 0.018  (rounded).

     The number in the intersection of column "better" and the row "Democrat" is related to the total.
</pre>

Solved, with all necessary explanations.