Apply and interpret the general Multiplication Rule with conditional probability.
Compare matched independent and dependent joint probabilities
Problem
Compute two red cards with replacement as \((26/52)^{2}\) and without replacement as \((26/52)(25/51)\). Compare the results.
Big Picture
What this problem is really about
Replacement determines whether the second draw resets or changes the deck. We’ll use the same first-red probability in both experiments, keep the second rate unchanged with replacement, update both counts without replacement, compute each joint product, and compare the exact fractions.
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