Conditional Probability – Venn + Tree Diagrams Review

Students will use a two-circle Venn diagram to find subset counts, such as how many students study only one of two languages.

Students will write or complete shaded-region expressions for a Venn diagram using union, intersection, and complement notation.

Students will draw and label a tree diagram for a without-replacement probability scenario, multiplying branch probabilities to find outcome probabilities.

Review union, intersection, and complement set notation before assigning the shaded-region problems, since students fill in or describe regions using this vocabulary.

Work through the marble tree-diagram example as a class first, since correctly adjusting the second draw's probability after removing a marble is the step students most often miss.

Use the five-page answer key to spot-check the algebra-heavy Venn diagram problem (31 students split across two activities), since an early miscount there affects every sub-question that follows.

Venn diagram interpretation — reading subset counts and regions from a two-circle diagram of overlapping categories.

Set notation — describing or filling Venn diagram regions using union, intersection, and complement.

Tree diagram construction — drawing and labeling branch probabilities for a without-replacement scenario, then multiplying along branches for outcome probabilities.