Conditional probability is “given that.” Restrict the sample space to the given group, then count inside it. Independent events do not change each other’s chances, in independent events.
The given is the new whole
“Among juniors, what fraction take Spanish” uses the junior total, not the table total. Two-way tables are built for this, in two-way tables. Mutually exclusive events cannot both happen, in mutually exclusive events.
The short list is in ACT Math formulas.
The bottom line
Given that: shrink the denominator to the given group, then count.
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