Question 1173589: Please I need help with this problem, i just don't know how to solve it correctly...
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 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:
P(affiliated with neither party) =
P(worse) =
P(worse|affiliated with neither party) =
P(affiliated with neither party|worse) =
P(affiliated with neither party and worse) =
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! make a table such as the one shown below:
republican democrat none total
better 38 12 21 71
same 104 87 90 281
worse 44 137 118 299
total 186 236 229 651
p(worse) is the total number of adults who said worse divided by the total number of adults.
that would be 299 / 651 = .4592933948 = .459
p(worse given none) is the total number of adults who were not affiliated with any party and said worse, divided by the total number of adults who were not affiliated with any party.
that would be 118 / 229 = .5152838428 = .515
p(none given worse) is the total number of adults who said worse and were not affiliated with any party, divided by the total number of adults who said worse.
that would be 118 / 299 = .3946488294 = .395
p(none and worse) is the total number of adults who were not affiliated with any part and, at the same time, said worse, divided by the total number of adults.
that would be 118 / 651 = .1812596006 = .181
the formula for p(a given b) is equal to p(a and b) / p(b)
from the table, .....:
p(worse and none) = 118 / 651 = .1812596006
p(none) = 229 / 651 = .3517665131
formula for p(worse given none) would be:
p(worse given none) = p(worse and none) / p(none) = .1812596006 / .3517665131 = .5152838428 = .515
this agrees with what the table showed when you analyzed p(worse given none) as shown below:
p(worse given none) is the total number of adults who were not affiliated with any party and said worse, divided by the total number of adults who were not affiliated with any party.
that would be 118 / 229 = .5152838428 = .515
i'm reasonably sure these are all correct.
give it a go and let me know how you did.
if any of these are not correct, let me know and i'll look at them again.
theo
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