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

• 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.

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.