Understand conditional probability and connect independence to unchanged conditional probabilities.
Use conditional probability for two draws without replacement
Problem
Find the probability of \(\text{two}~\text{red}~\text{cards}\) without replacement by multiplying \(26/52\) for the first red card by \(25/51\) for the second.
Big Picture
What this problem is really about
Without replacement, the second-draw probability must reflect the changed deck. We’ll compute the first favorable probability, update both favorable and total counts after that outcome, multiply along the conditional path, reduce the product, and avoid reusing the original fraction.
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