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PROBABILITY · LESSON 13

Probability Final Checkpoint

Complete an exam-style assessment across the complete final topic.

⏱️ 45–58 min 📘 Checkpoint 🎲 Visual models included

Final Probability Checkpoint

Section A: Foundations

  1. Define experiment, outcome and event.
  2. Place 0.8 on the probability scale and describe its likelihood.
  3. A fair spinner has 8 equal sectors, 3 yellow. Find P(yellow).
  4. In 200 trials an event happens 74 times. Find experimental probability.

Section B: Combined Events

  1. Two fair coins are tossed. Find P(exactly one head).
  2. Two dice are rolled. Find P(sum greater than 10).
  3. P(A)=0.6, P(B)=0.45 and P(A∩B)=0.2. Find P(A∪B).
  4. Independent events have P(A)=0.3 and P(B)=0.7. Find P(A∩B).

Section C: Trees and Applications

  1. A bag contains 6 red and 4 blue counters. Two are selected with replacement. Find P(two red).
  2. Repeat without replacement.
  3. Find P(at least one blue without replacement).
  4. An event has probability 0.14. Find expected frequency in 600 trials.
  5. Explain why expected and observed frequencies need not match exactly.

✅ Check Your Work

Show answers and working
  1. Experiment: uncertain process; outcome: one possible result; event: one or more outcomes of interest.
  2. 0.8 lies near certainty and may be described as very likely.
  3. 3/8.
  4. 74/200=37/100=0.37.
  5. HT or TH: 1/4+1/4=1/2.
  6. Sums 11 or 12: 3/36=1/12.
  7. 0.6+0.45−0.2=0.85.
  8. 0.3×0.7=0.21.
  9. 6/10×6/10=36/100=9/25.
  10. 6/10×5/9=30/90=1/3.
  11. 1−P(two red)=1−1/3=2/3.
  12. 0.14×600=84.
  13. Expected frequency is a long-run model; random variation changes observed results in a particular experiment.

🎯 Final Interactive Checkpoint

Answer five randomly selected probability questions.

Score: 0/0

Revision Guidance and Readiness