Compute conditional probability as the fraction of one event's outcomes that also belong to another event.
Compute conditional probability from a finite sample space by restricting to the given event
Problem
For two coins, restrict the sample space to outcomes with first toss heads, then count the two-head outcomes within that set.
Big Picture
What this problem is really about
Conditional probability can be computed by rebuilding the sample space inside the known event. We’ll retain only two-toss outcomes whose first toss is heads, count those that also contain two heads, and form a favorable-to-restricted-total ratio. Listing the reduced outcome set makes both the new denominator and qualifying numerator directly checkable.
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