More pitching: A baseball pitcher threw 3553 pitches during part of a recent season. Of these, 1597 were thrown with no strikes on the batter, 921 were thrown with one strike, and 1035 were thrown with two strikes.

Question

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

Answer 1

To find the probability that a baseball pitch is thrown with no strikes, we can use the formula for probability:

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

In this case, the number of favorable outcomes (pitches thrown with no strikes) is 1597, and the total number of outcomes (total pitches thrown) is 3553.

So, the probability \( P \) that a pitch is thrown with no strikes is:

\[ P(\text{no strikes}) = \frac{1597}{3553} \]

Now, we can calculate this probability:

\[ P(\text{no strikes}) \approx \frac{1597}{3553} \approx 0.4492 \]

Rounding to four decimal places, the probability that a baseball pitch is thrown with no strikes is:

\[ \boxed{0.4492} \]

Answer 2

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

Answer 3

To find the probability that a baseball pitch is thrown with fewer than two strikes, we need to consider the pitches thrown with no strikes and those thrown with one strike. We can calculate it using the following steps:

1. Count the number of pitches with fewer than two strikes:

   • Pitches with no strikes: 1597
   • Pitches with one strike: 921

   So, the total number of pitches with fewer than two strikes is:

   \[ 1597 + 921 = 2518 \]

2. Calculate the total number of pitches:

   • Total pitches thrown: 3553

3. Calculate the probability: Using the formula for probability:

   \[ P(\text{fewer than two strikes}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2518}{3553} \]

Now, we can calculate this probability:

\[ P(\text{fewer than two strikes}) \approx \frac{2518}{3553} \approx 0.7084 \]

Rounding to four decimal places, the probability that a baseball pitch is thrown with fewer than two strikes is:

\[ \boxed{0.7084} \]