What is the chance of getting a Red Cabbage in year 1?

Solution 1:

You are guaranteed to get Red Cabbage in year one if you enable the correct option.

As of version 1.5, you can choose to enable the Advanced Option: Guarantee Year 1 Completable by clicking on its checkbox.

This ensures that the Traveling Merchant sells a Red Cabbage seed during the first year.

Solution 2:

• According to this Reddit thread, you have

  a probability of 55,5% for getting at least one Red Cabbage within a year or 32,5% for getting Red Cabbage seeds once.

  (As mentioned in the comments, the values used only differ insignificantly from the actual values.)

• In that same thread, someone mentions using the Stardew Predictor to get an apparently good idea of what items you will get: using this you could see whether or not Red Cabbage will be available to you.