Question

P(A or B)=P(A) + P(B)-P(A and B)

P(A and B)=P(A)xP(B|A)
P(B|A)=P(A and B)
P(A)
In a Pew poll of American voters, almost 80% of Democrats say the government
shutdown is a "very serious problem for the country, while just 35% of Republicans feel
the same. 54% of the people polled were Democrats and 46% were Republicans.
(a) Overall, what percentage of American voters say the government shutdown is a
"very serious" problem for the country?
%
Answer=
(b) Set up a 2x2 probability table. Round all percentages to 2 decimal places.
Democrat
Republican
Total
Serious
P(A and B)=P(A)x P(B) (if independent)
Not Serious
Total
%
%
%
%
%
%
%
%
%

Answer 1

Answer:For part (a), the overall percentage of American voters who say the government shutdown is a "very serious problem for the country" can be calculated as follows:

P(A) = 54% (probability of being a Democrat)

P(B|A) = 80% (probability of saying the shutdown is a "very serious problem" given that the person is a Democrat)

P(A and B) = P(A) * P(B|A) = 54% * 80% = 43.2%

P(B) = 35% (probability of saying the shutdown is a "very serious problem" for Republicans)

P(A|B) = (P(A and B) / P(B)) = (43.2% / 35%) = 123.14%

P(A or B) = P(A) + P(B) - P(A and B) = 54% + 35% - 43.2% = 45.8%

Therefore, the overall percentage of American voters who say the government shutdown is a "very serious problem for the country" is 45.8%.

For part (b), the 2x2 probability table can be set up as follows:

Serious Not serious Total

Democrat 43.2% 6.8% 50%

Republican 10.5% 35.5% 46%

Total 53.7% 42.3% 100%

Explanation: