For equally likely outcomes, probability is the number of favorable outcomes divided by the total number of possible outcomes. The phrase equally likely matters: counting categories is not enough when those categories have different chances.
Start with a single draw
A bag contains three red tokens and two blue tokens, all otherwise identical. On a random draw, the probability of red is 3/5. The two color names do not make the probability one-half, because the colors have different numbers of tokens.
Replacement changes the next draw
If you draw a red token, replace it and mix the bag, the next draw still has a red probability of 3/5. The probability of two reds is 3/5 × 3/5 = 9/25.
Without replacement, a first red leaves two red tokens among four total. The probability of two reds is then 3/5 × 2/4 = 3/10. Read this condition before calculating.
Use the complement
For two draws with replacement, the probability of at least one red is one minus the probability of no reds. Both draws would need to be blue to have no reds, with probability 2/5 × 2/5 = 4/25.
Therefore at least one red has probability 21/25. This avoids separately counting exactly one red and exactly two reds.
Do not assume independence
Multiplying unchanged probabilities is appropriate only when the conditions justify it. Drawing without replacement changes the bag. A question about linked events may require conditional probabilities rather than treating each event as a fresh copy.
Make two final checks
A probability must lie between zero and one. Also ask whether the answer has the right direction: removing a red token should lower the chance of another red in this bag. A numerical result that contradicts that basic relationship deserves another look, even if the arithmetic itself seems tidy.