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
democrat	12	87	137
none	21	90	118

express your answers as a decimal and round to four decimal places (in other words, type 0.1235, not 12.35% or 0.123456).

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

p(democrat) =

p(worse) =

p(worse|democrat) =

p(democrat|worse) =

p(democrat and worse) =

Explanation:

Step1: Calculate total number of adults

The total number of adults is the sum of all values in the table. $38 + 104+44 + 12+87 + 137+21+90+118=651$.

Step2: Calculate P(Democrat)

The number of Democrats is $12 + 87+137 = 236$. So $P(\text{Democrat})=\frac{236}{651}\approx0.3625$.

Step3: Calculate P(worse)

The number of people who think the economy is getting worse is $44 + 137+118 = 299$. So $P(\text{worse})=\frac{299}{651}\approx0.4593$.

Step4: Calculate P(worse|Democrat)

By the formula for conditional - probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Here, $P(\text{worse}|\text{Democrat})=\frac{\text{Number of Democrats who think worse}}{\text{Number of Democrats}}=\frac{137}{236}\approx0.5805$.

Step5: Calculate P(Democrat|worse)

$P(\text{Democrat}|\text{worse})=\frac{\text{Number of Democrats who think worse}}{\text{Number of people who think worse}}=\frac{137}{299}\approx0.4582$.

Step6: Calculate P(Democrat and worse)

$P(\text{Democrat and worse})=\frac{\text{Number of Democrats who think worse}}{\text{Total number of adults}}=\frac{137}{651}\approx0.2105$.

Answer:

P(Democrat) = 0.3625
P(worse) = 0.4593
P(worse|Democrat) = 0.5805
P(Democrat|worse) = 0.4582
P(Democrat and worse) = 0.2105