To fill in the blanks with appropriate modal verbs, let's consider the context of each sentence:
might - "Sarah's studying" is not certain, so use "might."
- "Where’s Sarah? She might be very busy."
will certainly - To indicate certainty in the future.
- "He will certainly meet us by the lake."
may - Indicates possibility.
- "The water in the lake may be very cold."
may - Indicates possibility.
- "Jack may still be at the office doing some urgent work."
might - Indicates a lower probability or uncertainty.
- "He hasn’t called me yet. He might still be busy."
will definitely - Shows certainty that an event will happen.
- "She will definitely go on a boat trip across the Mediterranean Sea. She hasn’t planned it yet."
will certainly - Shows certainty about future plans.
- "They will certainly be out of town for the weekend."
will probably - Indicates likelihood without complete certainty.
- "She has promised me – she will probably phone me in the afternoon."
may - Indicates a less certain possibility.
- "The taxi may still be stuck in traffic at the moment."
will probably - A probable future event.
- "They will probably be travelling at the moment."
These choices reflect the level of certainty or possibility appropriate for each context.