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Grade 12 Challenge: Probability Paradoxes Worksheet with Answers

Grade 12 (US) · Year 13 (UK) · Class 12 (India) · Math

Unit 6: Going FurtherReal-World ChallengesChallenge

Results that surprise even adults: medical false positives, the birthday problem, Monty Hall, overbooked flights and gambler's ruin. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Challenge: Probability Paradoxes

Grade 12 · Math

Score___ / 12

Name

Class

Date

Learning goal: Real-World Challenges

Directions: Solve each problem. Show your work, then write your answer in the box.

  1. 1

    Monty Hall with 10 doors: you pick one, then the host (who knows where the car is) opens 8 of the others, all goats. If you switch to the last closed door, what is your probability of winning?

    Show your work
    Answer
  2. 2

    Monty Hall with 10 doors: one hides a car. You pick a door; the host, who knows where the car is, opens one other door showing a goat. You switch to one of the other unopened doors at random. What is your probability of winning the car?

    Show your work
    Answer
  3. 3

    You roll a fair 4-sided die until every face has appeared at least once. On average, how many rolls does that take? Give your answer to 1 decimal place.

    Show your work
    Answer
  4. 4

    You roll a fair 6-sided die until every face has appeared at least once. On average, how many rolls does that take? Give your answer to 1 decimal place.

    Show your work
    Answer
  5. 5

    You have $14 and bet $1 at a time on a fair coin toss. You stop when you reach $48 or go broke. What is the probability you reach $48? Give a fraction.

    Show your work
    Answer
  6. 6

    A small plane has 18 seats but the airline sells 19 tickets. Each passenger independently shows up with probability 0.85. What is the probability that more passengers show up than there are seats? Give your answer to 3 decimal places.

    Show your work
    Answer
  7. 7

    You roll a fair 8-sided die until every face has appeared at least once. On average, how many rolls does that take? Give your answer to 1 decimal place.

    Show your work
    Answer
  8. 8

    A small plane has 20 seats but the airline sells 22 tickets. Each passenger independently shows up with probability 0.85. What is the probability that more passengers show up than there are seats? Give your answer to 3 decimal places.

    Show your work
    Answer
  9. 9

    You have $29 and bet $1 at a time on a fair coin toss. You stop when you reach $67 or go broke. What is the probability you reach $67? Give a fraction.

    Show your work
    Answer
  10. 10

    A disease affects 1 in 1000 people. A test detects it 90% of the time but also gives a false positive for 2% of healthy people. You test positive. What is the probability you actually have the disease? Give a percentage to 1 decimal place.

    Show your work
    Answer
  11. 11

    A small plane has 18 seats but the airline sells 20 tickets. Each passenger independently shows up with probability 0.85. What is the probability that more passengers show up than there are seats? Give your answer to 3 decimal places.

    Show your work
    Answer
  12. 12

    In a room of 10 people, what is the probability that at least two share a birthday? Ignore leap years and give a percentage to 1 decimal place.

    Show your work
    Answer

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Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/12/challenge_probability_paradoxes

Answer key (click to show)
  1. 1.9/10
  2. 2.9/80
  3. 3.8.3
  4. 4.14.7
  5. 5.7/24
  6. 6.0.046
  7. 7.21.7
  8. 8.0.137
  9. 9.29/67
  10. 10.4.3%
  11. 11.0.176
  12. 12.11.7%

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