Based on a poll, $40 \%$ of adults believe in reincarnation. Assume that 5 adults are randomly selected, and find the indicated probability. Complete parts (a) through (d) below. a. What is the probability that exactly 4 of the selected adults believe in reincarnation? The probability that exactly 4 of the 5 adults believe in reincarnation is 0.077 . (Round to three decimal places as needed.) b. What is the probability that all of the selected adults believe in reincarnation? The probability that all of the selected adults believe in reincarnation is (Round to three decimal places as needed.)

Step 1 ：This problem is a binomial probability problem. The binomial distribution model is appropriate for a quantitative variable that counts the number of successes in a fixed number of trials of a binary, or two-outcome, situation. In this case, the two outcomes are 'believes in reincarnation' and 'does not believe in reincarnation'.

Step 2 ：The probability of success (believing in reincarnation) is given as \(0.4\). The number of trials is \(5\) (the number of adults selected).

Step 3 ：For part (a), we are asked to find the probability of exactly \(4\) adults believing in reincarnation. The probability that exactly \(4\) of the \(5\) adults believe in reincarnation is \(0.077\).

Step 4 ：For part (b), we are asked to find the probability of all \(5\) adults believing in reincarnation, which is the same as finding the probability of \(5\) successes in \(5\) trials.

Step 5 ：Using the binomial probability formula, where \(p = 0.4\), \(n = 5\), and \(k = 5\), the probability is calculated to be \(0.010240000000000003\).

Step 6 ：Rounding to three decimal places as needed, the final answer is: The probability that all of the selected adults believe in reincarnation is \(\boxed{0.010}\).