Seventh Grade · Math · week 34

Compound events and tree diagrams

Find the sample space and probability of a compound event using tree diagrams or organized lists, and verify with the multiplication rule.

A compound event combines two or more simple events, like flipping a coin AND rolling a die. A tree diagram or an organized list shows every possible combined outcome -- the full sample space -- so you can count exactly how many outcomes exist and how many match what you want.

For independent events (one does not affect the other), there is a shortcut: P(A and B) = P(A) x P(B). This multiplication rule always agrees with counting the full sample space directly -- it is worth checking both ways until you trust the shortcut.

📋 For the teacher
Teach it (10–15 min):
  • Draw an actual tree diagram together at least once -- branches for the first event, then branches off each of those for the second event.
  • Count the full sample space directly at first, then introduce the multiplication rule as a confirmed shortcut, not a replacement for understanding.
  • Watch for ordered versus unordered questions -- "red then blue" is different from "one red and one blue in any order."
  • Practice the multiplication rule on a compound event with three parts, not just two, once two-part events feel solid.
Talk about it:
  • How does a tree diagram help you count a sample space accurately?
  • Why does the multiplication rule work for independent events?
  • How is "red then blue" different from "one red and one blue, in either order"?

Mastery looks like: They correctly find the sample space of a compound event and compute its probability, confirming the result with the multiplication rule.

Common stumbles: Missing outcomes when listing the sample space by hand; confusing an ordered outcome with an unordered one.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

MultiplicationEqual groups and arrays make products finally click.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
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