If two events do not affect each other, multiply their probabilities. P(A and B) = P(A) × P(B). A 1/4 chance and a 1/8 chance both happening is 1/32. Probability as a set is in probability problems.
Independent versus without replacement
Two coin flips are independent. Drawing two cards without putting the first back is not: the second probability changes. Counting outfits or menus is the counting principle, in the counting principle.
Expected value weights outcomes by probability, in expected value. Statistics overall is in statistics and probability.
The bottom line
Independent: multiply. If the first draw changes the second, do not.
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