In a survey of U.S. adults with a sample size of 2062,311 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. The probability that both adults say Franklin Roosevelt was the best president since World War II is (Round to three decimal places as needed.)

Given that there are 2062 adults in the sample and 311 of them said Franklin Roosevelt was the best president since World War II, we can calculate the probability that both adults selected at random from this sample say Franklin Roosevelt was the best president since World War II. Let's denote: - \( N \) as the total number of adults in the sample (2062), - \( n \) as the number of adults who said Franklin Roosevelt was the best president since World War II (311), - \( P \) as the probability that an adult selected at random from the sample says Franklin Roosevelt was the best president since World War II. The probability that the first adult selected says Franklin Roosevelt was the best president since World War II is \( P = \frac{n}{N} \). The probability that the second adult selected says Franklin Roosevelt was the best president since World War II, given that the first adult said so, is \( P' = \frac{n-1}{N-1} \). Therefore, the probability that both adults say Franklin Roosevelt was the best president since World War II is the product of these two probabilities: \[ P_{\text{both}} = P \times P' = \frac{n}{N} \times \frac{n-1}{N-1} \] Now, we can calculate this probability. Calculate the value by following steps: - step0: Calculate: \(\frac{\frac{311}{2062}\left(311-1\right)}{\left(2062-1\right)}\) - step1: Remove the parentheses: \(\frac{\frac{311}{2062}\left(311-1\right)}{2062-1}\) - step2: Subtract the numbers: \(\frac{\frac{311}{2062}\times 310}{2062-1}\) - step3: Multiply the numbers: \(\frac{\frac{48205}{1031}}{2062-1}\) - step4: Subtract the numbers: \(\frac{\frac{48205}{1031}}{2061}\) - step5: Multiply by the reciprocal: \(\frac{48205}{1031}\times \frac{1}{2061}\) - step6: Multiply the fractions: \(\frac{48205}{1031\times 2061}\) - step7: Multiply: \(\frac{48205}{2124891}\) The probability that both adults selected at random from the sample say Franklin Roosevelt was the best president since World War II is approximately 0.0227 (rounded to three decimal places).