Use permutations and combinations to compute probabilities of compound events and solve problems.
Evaluate two explicit counting strategies for equivalence
Problem
For at least \(\text{one}\) ace in a \(5\text{-}\text{card}\) hand, compare the explicit direct setup \([\Sigma~\text{from}~k=1~\text{to}~4~\text{of}~C(4,k)C(48,5-k)]/C(52,5)\) with the complement setup \(1-C(48,5)/C(52,5)\).
Big Picture
What this problem is really about
Two probability strategies can be compared only after fixing a common sample space. We’ll evaluate the disjoint direct cases, independently count and subtract the no-ace complement, place each favorable count over the same unordered-hand total, and compare the reduced results.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
