Use Classical Probability when:

• Drawing from a collection (balls, cards) without replacement
• Arrangements or selections
• Sample space is finite and outcomes are equally likely
• Events involve combinations/permutations

Use Binomial Distribution when:

• Fixed number of independent trials
• Each trial has exactly two outcomes $\frac{success}{failure}$
• Probability of success is constant across trials
• Question asks for probability of exactly/at least/at most k successes

Key difference: Classical probability counts outcomes from a single experiment. Binomial models repeated independent experiments with the same success probability.

Trap: Drawing WITH replacement from a bag → Binomial (trials are independent). Drawing WITHOUT replacement → Classical/Hypergeometric (trials are dependent).