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

To determine the probability that a baseball pitch is thrown with fewer than two strikes, we need to consider the outcomes of each pitch regarding strikes. Typically, in baseball, a pitch can result in different outcomes such as a strike, ball, or hit.

1. ### Break Down the Problem

• Identify all possible outcomes for a pitch in terms of strikes.
• Define the event of interest: fewer than two strikes, which includes zero or one strike.

2. ### Relevant Concepts

• Let's assume the probabilities of outcomes are as follows:
  • P(Strike) = p
  • P(Ball) = q = 1 - p
• Outcomes with fewer than two strikes:
  • 0 strikes (Ball)
  • 1 strike (Ball, Strike)

3. ### Analysis and Detail

• The probability of getting 0 strikes:
  • This happens if we have a Ball on the first pitch.
  • Therefore, P(0 strikes) = q
• The probability of getting 1 strike:
  • This happens if we have a Ball followed by a Strike, which could occur in two scenarios.
  • P(1 strike) = q * p

Total probability of fewer than two strikes: $P(\text{fewer than 2 strikes}) = P(0 \text{ strikes}) + P(1 \text{ strike}) = q + qp = q(1+p)$

4. ### Verify and Summarize

• Substitute values for p and q based on real-world data (if available) or hypothetical values.
• If p = 0.6 (60% chances for a strike), then q = 0.4, gives: $P(\text{fewer than 2 strikes}) = 0.4(1 + 0.6) = 0.4 \times 1.6 = 0.64$

Final Answer

The probability that a baseball pitch is thrown with fewer than two strikes is approximately $0.6400$ when rounded to four decimal places.