You don't have to memorize probability tables to be a good bridge player. That said, in order to make the best plan, you have to know which path is most likely to work. It's also sometimes helpful to know what to anticipate from each deal.
A good general rule is that if you are missing more than 4 cards: an odd number of cards tend to split evenly (so 5 cards will usually split 3-2) and an even number of cards will split oddly (so 6 cards will not split 3-3).
See if you can identify the best path in these common scenarios.
Which is most likely to work?
A simple finesse
Playing for suit to split 3-3
Playing for a suit to split 3-2
Holding 8 cards, missing the queen, playing the A and K and playing for the queen to drop.
Complaining to your partner that bridge is hard.
Which of these is most likely to produce 2 tricks for your side in notrump? Assume infinite entries/stoppers in the outside suits.
A43 opposite 7652
AJ10 opposite 752
AQ2 opposite 765
K62 opposite Q54
Which is the right way to play this suit based on the odds? Assume no entry problems or information from the bidding/play.
Play the ace and king
Play the ace and then finesse the jack
Finesse the jack (lead low towards the jack) the first time
Lead the J
A bidding question: which type of hand is most common?
Balanced hand (no singleton, no void, not two-doubletons)
Semi-Balanced hand (5-4-2-2 shape or 6-3-2-2)
Unbalanced hand (singleton, void, 7+ card suit)
How many deals would you need to play in order for it to be likely that you've played the same 13-card hand twice?
Way more than these
What level is most common for final contracts?
Which of these contracts is most likely to make?
A contract that depends on one finesse
A contract that depends on 1 of 2 finesses
A contract that will make if either a finesse works or a suit breaks 3-3
A contract that will make if a suit splits 2-2
A contract that that will make if your opponents don't notice you play the A twice