Which of the following problems did the Massachusetts Bay Colony face?

The Massachusetts Bay Colony faced several challenges during its existence. Among the options you've provided, the following problems are relevant:

1. **It experienced a struggling economy** - The colony faced economic difficulties at various points, particularly due to the challenges of establishing a new settlement, trade limitations, and occasional conflicts with Indigenous populations.

2. **It battled drought and food shortages** - The Massachusetts Bay Colony, like many early colonies, faced issues with food production, especially during harsh winters or when agricultural conditions were not favorable.

The other options, such as being burned in a rebellion or disappearing mysteriously, do not accurately describe the historical events related to the Massachusetts Bay Colony. The colony was not destroyed in a rebellion like some others, nor did it disappear mysteriously.