Explanation:

To understand the correct answer, let's break down the sentence and analyze each component.

The given sentence is: "They _______________ (play) for three hours by noon."

Subject:
The subject of the sentence is "They." It refers to a group of people who are performing the action.

Verb tense:
The verb tense used in the sentence is the future perfect continuous tense. This tense is used to describe an ongoing action that will be completed in the future before a specific time.

Future perfect continuous tense:
The future perfect continuous tense is formed by using "will have been" followed by the present participle form of the verb ("-ing" form). This tense is used to describe an action that will start in the future, continue for a specific duration, and be completed before a certain time in the future.

By noon:
The phrase "by noon" indicates the specific time until which the action will be completed. In this case, the action of playing will be completed before noon.

Putting it all together:
Based on the given sentence, the correct answer is "will have been playing." This indicates that the group of people will start playing in the future, continue playing for three hours, and complete playing before noon.

Alternative options:
- "will be playing": This option suggests that the group of people will start playing in the future and continue playing until noon, but it does not convey the duration of three hours.
- "will have played": This option suggests that the group of people will start playing in the future and complete playing before noon, but it does not convey the ongoing nature of the action.

Therefore, the correct answer is "will have been playing" as it accurately describes the ongoing action of playing for three hours before noon.