According to a certain news poll, 71% 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.) HINT [See Quick Examples 4 and 5.]

Given that according to a certain news poll, 71% agreed that it should be the government's responsibility to provide a decent standard of living for the elderly,

Let A be the event that it should be the government's responsibility to provide a decent standard of living for the elderly, and B the event that it would be a good idea to invest part of their Social Security taxes on their own

P(B) = 41%=0.41

A and B are independent

Hence P(both)=[tex]0.77(0.41) = 0.3157\\[/tex]

the probability that a person agreed with both propositions

= Probability for both A and B

= P(A) P(B) since A and B are independent

= 0.3157