Start with the experiment and its assumptions
List the possible outcomes and identify the event you care about. The fraction favorable outcomes/total outcomes applies directly when the individual outcomes are equally likely.
Track what changes between events
Replacing a drawn object can restore the original probabilities; keeping it out changes the available objects. State that choice before combining probabilities across draws.
A mistake to avoid
Two named categories are not automatically equally likely. A bag with more red objects than blue does not give a one-half chance of each color just because there are two color names.
Worked example
Draw from a bag with 3 red and 2 blue counters
If every counter is equally likely to be drawn, P(red) = 3/5. If a red counter is drawn and not replaced, the remaining bag has 2 red counters out of 4, so the next draw’s chance of red is 2/4.