Question In a recent baseball season, Ron was hit by pitches 21 times in 602 plate appearances during the regular season. Assume that the probability that Ron gets hit by a pitch is the same in the playoffs as it is during the regular season. In the first playoff series, Ron has 23 plate appearances. What is the probability that Ron will get hit by a pitch exactly once? Use Excel to find the probability. - Round your answer to three decimal places. Provide your answer below:

Step 1 ：First, we need to calculate the probability of success, which is the number of times Ron was hit by a pitch divided by the number of plate appearances. This gives us \( p = \frac{21}{602} = 0.03488372093023256 \).

Step 2 ：Next, we use the binomial probability formula to find the probability of exactly one success in 23 trials. The formula is \( P(X=k) = C(n, k) \cdot p^k \cdot (1-p)^{n-k} \), where \( n \) is the number of trials, \( k \) is the number of successes, \( p \) is the probability of success, and \( C(n, k) \) is the number of combinations of \( n \) items taken \( k \) at a time.

Step 3 ：Substituting the given values into the formula, we get \( P(X=1) = C(23, 1) \cdot (0.03488372093023256)^1 \cdot (1-0.03488372093023256)^{23-1} \).

Step 4 ：Calculating the above expression, we find that the probability that Ron will get hit by a pitch exactly once in the first playoff series is approximately 0.367.

Step 5 ：Rounding to three decimal places, the final answer is \(\boxed{0.367}\).