According to a New York Times/CBS poll released in March, 2005, 78% agreed that it should be the government's responsibility to provide a decent standard of living for the elderly, and 41% agreed that it would be a good idea to invest part of their Social Security taxes on their own. If agreement with one of these propositions is independent of agreement with the other, what is the probability that a person agreed with both propositions (Round your answer to two decimal places.)
A)0.21
B) 0.33
C) 0.32
D) 0.37
E) 0.42

Question

According to a New York Times/CBS poll released in March, 2005, 78% agreed that it should be the government's responsibility to provide a decent standard of living for the elderly, and 41% agreed that it would be a good idea to invest part of their Social Security taxes on their own. If agreement with one of these propositions is independent of agreement with the other, what is the probability that a person agreed with both propositions  (Round your answer to two decimal places.)  
A)0.21
B) 0.33
C) 0.32
D) 0.37
E) 0.42

Quizplus · Accepted Answer

We can use the formula P(A and B) = P(A) x P(B) if A and B are independent events. 
Let A be the event of agreeing that it's the government's responsibility to provide a decent standard of living for the elderly (P(A) = 0.78) 
Let B be the event of agreeing that it would be a good idea to invest part of their Social Security taxes on their own. (P(B) = 0.41)
Since the prompt tells us that agreement with one of these propositions is independent of agreement with the other, we can use the formula:
P(A and B) = P(A) x P(B) = 0.78 x 0.41 = 0.3198
Rounded to two decimal places, this gives us a probability of 0.32, which is answer choice C.

According to a New York Times/CBS Poll Released in March