Casework and Law of Total Probability

You have a lunch break from 12pm to 1:30pm, during which at any point you can go and get food from your favorite dining spot.

• If you go from 12pm to 12:30pm, there is a $50\%$ chance you'll have to wait in line for more than $10$ minutes.
• If you go from 12:30pm to 1pm, there is a $70\%$ chance.
• If you go from 1pm to 1:30pm, there is a mere $20\%$ chance.

You are equally likely to pick any of these three timeslots to grab lunch.