According to a certain news poll 78 agreed that it should be

According to a certain news poll, 78% agreed that it should be the government\'s responsibility to provide a decent standard of living for the elderly, and 34% 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 on Independence.]

Solution

Probability that a person agreed with both proposition = prob. [ he agreed that  it should be the government\'s responsibility to provide a decent standard of living for the elderly AND he agreed that it would be a good idea to invest part of their Social Security taxes on their own ]........
= prob. [ he agreed that  it should be the government\'s responsibility to provide a decent standard of living for the elderly] * prob. [ he agreed that it would be a good idea to invest part of their Social Security taxes on their own].....
(since, the events are independent)

= (78/100) ( 34 /100) = 0.2652