So it makes no sense to eat 9k to avoid a chance at spending 4k.

Let's say the car has a 25% chance of the transmission going out.

You have an expected gain of 8k by keeping the car and expected loss of 8k by getting rid of it.

This isn't always the best way to frame situations, especially if the loss is catastrophic (for example say you have a 1% chance at a 500k loss) but since the loss in this case is less than what you are spending up front to avoid it, it makes no sense to do so.

This is like paying 1000 dollars a month to insure something that is worth 5000 dollars.