Question: In Plants vs Zombies, are there strategies that make it more probable to have certain plants (for your Zen Garden)?

How does the game decide which plant is given?

Answer: 
I'll assume you are talking about plants that you find for your zen garden (the only other option is the plants unlocked while playing the game's adventure mode, and those have a set order which never changes).

There is no way to increase the probability of receiving a certain kind of plant for your zen garden. The type of plant received is completely random.

Looking around the internet, it is said that while there is an equal chance to get all types of plants on Survival: Endless, other minigames have a higher tendency to produce plants you first unlock in the area where the minigame is played (night levels will produce more night-time plants, for example). This is not backed up by any hard evidence, however, and I can't really say I've noticed this during the countless hours my wife strived to acquire every possible plant for her garden.
Based on the comment from [Guillaume Coté](https://gaming.stackexchange.com/questions/26034/how-to-obtain-a-specific-plant-for-the-zen-garden/31908?noredirect=1#comment177519_31908), going to add a clear answer

Short answer: **NO**, you can't pick an **specific** plant. But there are someways to get a **specific type** of plant (aquatic, mushrooms ...)

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I once read that: *(lost link)*

* Aquatic levels (pool) increase your chances to get aquatic plants.
* Night levels (night) increase your chances to get mushroom plants.

But the best way to get Zen Garden plants is to play Survival: Endless, as all plants can be obtained in it and it is the level with the greatest number of zombies.