According to a daily newspaper, the probability is about 066 that the favorite in a horse race will finish in the money (first, second, or third place). Complete parts (a) th a. In the next five races, what is the probability that the favorite finishes in the money exactly twice? The probability that the favonite finishes in the money exactly twice is 0171 (Round to three decimal places as needed) b. In the next five races, what is the probability that the favonite finishes in the money exactiy four times? The probability that the favorite finishes in the money exactly four times is 0.323 (Round to three decimal places as needed) c. In the next five races, what is the probability that the favorite finishes in the money at least four times? The probability that the favorite finishes in the money at least four times is 0.448 (Round to three decimal places as needed) d. In the next five races, what is the probability that the favonite finishes in the money between two and four times, inclusive? The probability that the favorite finishes in the money between two and four times, inclusive, is $\square$ (Round to three decimal places as needed)

Step 1 ：The problem is asking for the probability that the favorite horse finishes in the money (first, second, or third place) exactly twice in the next five races. This is a binomial probability problem, where the number of trials is 5 (the number of races), the number of successes we want is 2 (the horse finishing in the money twice), and the probability of success on each trial is 0.66 (the probability that the horse finishes in the money in any given race).

Step 2 ：The formula for binomial probability is: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\), where \(P(X=k)\) is the probability of \(k\) successes in \(n\) trials, \(C(n, k)\) is the number of combinations of \(n\) items taken \(k\) at a time, \(p\) is the probability of success on each trial, and \(n\) is the number of trials.

Step 3 ：We can plug the values from the problem into this formula to find the answer. Here, \(n = 5\), \(k = 2\), and \(p = 0.66\).

Step 4 ：Calculating the above values, we get the probability as 0.171208224.

Step 5 ：Rounding to three decimal places as needed, we get the final answer.

Step 6 ：Final Answer: The probability that the favorite horse finishes in the money exactly twice in the next five races is \(\boxed{0.171}\).