Regarding finesses for a missing queen in a key (e.g. trump suit), there is a proverb of "eight ever [always] nine never." Instead, one is supposed to play for a drop. (This, and most other proverbs need to be taken with grain of salt).
A "blind" finesse (without further information), is 50-50. If you have nine cards in a suit headed by the ace and king (and play them to drop the queen), your chances of success are 52.5%. That is, the opposing cards will fall 2-2. 40% of the time. Some 50% of the time, they will be split 3-1.And of these, the singleton will be the queen one-fourth of the time, or 12.5% of the total (40%+12.5%)= 52.5%.
But suppose you have one or more finesse possibilities. That is, you have AJxxx. Dummy has KTxx. Then you can lead one of your tops "blindly" and catch the queen 12.5% of the time. A finesse the other way would succeed 50% of the remaining times =.5*87.5% or 43.75%. The total chances of success would be (43.75+12.5%)=56.25%> 52.5%.
So a "drop" (top card) play followed by a finesse has an advantage over a pure drop (two top card plays), right? And wouldn't this be even more true if East or West showed strength by opening, meaning that you would finesse "around" him to one hand after playing the top honor in the other hand.
And wouldn't the exception be if you had only a "one way" finesse e.g. Axxxx opposite dummy's KTxx and East opened, meaning that the Q was probably "offside?