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

Students will calculate a conditional probability, such as P(sum = 7 | at least one die shows 3), from a two-dice sum chart.

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 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.

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

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

Conditional probability calculation — finding P(A | B) from a two-dice sum chart and from survey-style word problems.