Let’s solve this problem step by step:

Problem Breakdown:

• The probability of striking out is 45%, or $0.45$.
• The probability of not striking out is: $P(\text{Not Strike Out}) = 1 - 0.45 = 0.55$
• The player is up at bat 3 times in a row, and we want the probability that they will not strike out in all 3 at-bats.

Calculation:

For each at-bat, the events are independent, meaning the probability of not striking out remains the same each time. Thus, the probability of not striking out 3 times in a row is: $P(\text{Not Strike Out 3 Times}) = P(\text{Not Strike Out})^3 = 0.55^3$

Compute $0.55^3$:

$0.55^3 = 0.55 \times 0.55 \times 0.55 = 0.166375$

So, the probability is approximately: $16.6\%$

Final Answer:

The correct choice is 16.6%.

Would you like a more detailed explanation of any step? Let me know!

Related Questions:

1. What is the probability of striking out all 3 times in a row?
2. How would the probability change if the strikeout rate was 30% instead of 45%?
3. What is the probability of not striking out exactly 2 times in 3 at-bats?
4. If the player has 10 at-bats, what is the probability of striking out fewer than 3 times?
5. How can this problem be visualized using a probability tree?

Tip:

When solving probability questions involving repeated independent events, always raise the single-event probability to the power of the number of repetitions.