In a survey of U.S. adults with a sample size of 2048,357 said Franklin Roosevelt was the best president since World War II. Two U.S. adults are selected at random from this sample without replacement. Complete parts (a) through (d).
(a) Find the probability that both adults say Franklin Roosevelt was the best president since World War II.
Answer
Final Answer: The probability that both adults say Franklin Roosevelt was the best president since World War II is approximately \(\boxed{0.0303}\).
Step 1 ：The problem is asking for the probability that both randomly selected adults from the sample say Franklin Roosevelt was the best president since World War II. This is a problem of probability without replacement.
Step 2 ：The probability of the first adult saying Franklin Roosevelt was the best president is the number of adults who said Franklin Roosevelt was the best president divided by the total number of adults. So, \(\frac{357}{2048} = 0.17431640625\).
Step 3 ：Since we are selecting without replacement, the probability of the second adult also saying Franklin Roosevelt was the best president is the number of remaining adults who said Franklin Roosevelt was the best president divided by the remaining total number of adults. So, \(\frac{356}{2047} = 0.17391304347826086\).
Step 4 ：The final probability is the product of these two probabilities. So, \(0.17431640625 \times 0.17391304347826086 = 0.030315896739130432\).
Step 5 ：Final Answer: The probability that both adults say Franklin Roosevelt was the best president since World War II is approximately \(\boxed{0.0303}\).
