In the sentence, "Take an umbrella with you when you go out. It might rain later," the word "might" is used to convey the possibility of rain occurring later. It indicates uncertainty or a potential future event.

Here's an elaboration for each of the options:

1. "Must" would imply a strong obligation or necessity to take an umbrella, which may not be the case if the weather is uncertain.

2. "Will" would suggest a future certainty, implying that rain is expected, which might not be the intention of the statement.

4. "Can" doesn't fit in the context, as it doesn't express the possibility of rain, but rather the ability to take an umbrella.

Might is the most appropriate choice because it conveys the idea that rain is a possibility but not a certainty, aligning with the uncertainty of the situation.