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.
At least on the PC version of the game, if you play Hard Survival levels, you can improve your chances of getting specific plants. If you get a Zen Garden plant, it will be from a specific set plants, a list of 8 plants on most levels or 6 on Roof level. No other plant for your Zen Garden will show up on that level. The list of plants that can show up on each Hard Survival level is shown below.

* **Day Hard Survival:** Peashooter, Sunflower, Cherry bomb, Wall-nut,
Potato mine, Snow pea, Chomper, or Repeater
* **Night Hard Survival:** Puff-shroom, Sun-shroom, Fume-shroom, Grave
Buster, Hypno-shroom, Ice-shroom, or Doom-shroom
* **Pool Hard Survival:** Lily pad, Squash, Threepeater, Tangle kelp,
Jalepeno, Spikeweed, Torchwood, or Tall-nut
* **Fog Hard Survival:** Sea-shroom, Plantern, Cactus, Blover, Split pea,
Starfruit, Pumpkin, or Magnet-shroom
* **Roof Hard Level:** Cabbage-pult, Kernel-pult, Coffee bean, Garlic,
Umbrella leaf, or Melon-pult