Treasure Inspiration
Tree Diagrams & Combined Events
T

Tree Diagrams with Replacement and Without Replacement

Push a bit harder. Apply what you know to less familiar problems.

Mathematics · Medium

5

questions · ~4 min · 3 hints each (−5 pts)

Confidence tracking, 3-tier hints and instant feedback.

What you'll learn

Each question helps you build key knowledge and skills.

  • 1When items are replaced, probabilities stay the same for each pick.
  • 2When items are NOT replaced, probabilities change because the total number of items decreases.
  • 3To find the probability of 'at least one', use 1 minus the probability of 'none'.
  • 4Add branch probabilities together when more than one branch gives the desired outcome.

Question mix

A mix of question types to build your skills.

  • Short answer×4
  • True / False×1

Different question types help you think in different ways.

How it works

A simple 3-step process

  1. 1

    Rate your confidence

    Tell us how sure you feel before answering. It helps us understand your starting point.

  2. 2

    Use hints if stuck

    Get up to 3 helpful hints per question. Each hint costs 5 Treasure Points.

  3. 3

    See what went wrong

    Get instant feedback with clear explanations, so you can learn and improve.

Ready when you are

This takes about 4 minutes.