Question: More pitching: A baseball pitcher threw 3406 pitches during part of a recent season. Of these,…

More pitching: A baseball pitcher threw 3406 pitches during part of a recent season. Of these, 1421 were thrown with no strikes on the batter, 873 were thrown with one strike, and 1112 were thrown with two strikes.

Part 1 of 2

(a) What is the probability that a baseball pitch is thrown with no strikes? Round your answer to four decimal places.

\( P(\text{A baseball pitch thrown with no strikes}) = \)

Part: 1 / 2

Part 2 of 2

(b) What is the probability that a baseball pitch is thrown with fewer than two strikes? Round your answer to four decimal places.

\( P(\text{A baseball pitch thrown with fewer than two strikes}) = \)

Solution

Step 1: Identify the total number of pitches. \[ \text{Total number of pitches} = 3406 & \] Step 2: Determine the number of pitches with no strikes. \[ \text{Number of pitches with no strikes} = 1421 & \] Step 3: Calculate the probability of a pitch being thrown with no strikes. \[ P(\text{no strikes}) = \frac{1421}{3406} & \] Step 4: Compute the probability and round to four decimal places. \[ P(\text{no strikes}) \approx 0.4170 & \] --- Step 1: Identify the total number of pitches. \[ \text{Total number of pitches} = 3406 & \] Step 2: Determine the number of pitches with fewer than two strikes (no strikes or one strike). \[ \text{Number of pitches with fewer than two strikes} = 1421 + 873 = 2294 & \] Step 3: Calculate the probability of a pitch being thrown with fewer than two strikes. \[ P(\text{fewer than two strikes}) = \frac{2294}{3406} & \] Step 4: Compute the probability and round to four decimal places. \[ P(\text{fewer than two strikes}) \approx 0.6742 & \]