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Grade 11 Challenge: Probability Paradoxes Worksheet with Answers
Grade 11 (US) · Year 12 (UK) · Class 11 (India) · Math
Unit 8: 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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Practice Sheetaethelsystems.comChallenge: Probability Paradoxes
Grade 11 · Math
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Class
Date
Learning goal: Real-World Challenges
Directions: Solve each problem. Show your work, then write your answer in the box.
In a room of 30 people, what is the probability that at least two share a birthday? Ignore leap years and give a percentage to 1 decimal place.
Answer: 70.6%
- 1
A small plane has 18 seats but the airline sells 19 tickets. Each passenger independently shows up with probability 0.9. What is the probability that more passengers show up than there are seats? Give your answer to 3 decimal places.
Show your workAnswer - 2
Monty Hall with 4 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 workAnswer - 3
A small plane has 30 seats but the airline sells 32 tickets. Each passenger independently shows up with probability 0.9. What is the probability that more passengers show up than there are seats? Give your answer to 3 decimal places.
Show your workAnswer - 4
Monty Hall with 50 doors: you pick one, then the host (who knows where the car is) opens 48 of the others, all goats. If you switch to the last closed door, what is your probability of winning?
Show your workAnswer - 5
You have $6 and bet $1 at a time on a fair coin toss. You stop when you reach $40 or go broke. What is the probability you reach $40? Give a fraction.
Show your workAnswer - 6
A small plane has 20 seats but the airline sells 21 tickets. Each passenger independently shows up with probability 0.9. What is the probability that more passengers show up than there are seats? Give your answer to 3 decimal places.
Show your workAnswer - 7
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 workAnswer - 8
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 workAnswer - 9
Monty Hall with 5 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 workAnswer - 10
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 workAnswer - 11
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 workAnswer - 12
A small plane has 18 seats but the airline sells 21 tickets. Each passenger independently shows up with probability 0.9. What is the probability that more passengers show up than there are seats? Give your answer to 3 decimal places.
Show your workAnswer
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Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/11/challenge_probability_paradoxes
Answer key — Challenge: Probability Paradoxes (Grade 11)
- 1.0.135
- 2.3/8
- 3.0.156
- 4.49/50
- 5.3/20
- 6.0.109
- 7.9/10
- 8.21.7
- 9.4/15
- 10.14.7
- 11.9/80
- 12.0.648
Answer key (click to show)
- 1.0.135
- 2.3/8
- 3.0.156
- 4.49/50
- 5.3/20
- 6.0.109
- 7.9/10
- 8.21.7
- 9.4/15
- 10.14.7
- 11.9/80
- 12.0.648
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