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Probability in FunTrivia Trivia Quiz

Ten probability questions based around FunTrivia. You might want a calculator handy for some questions and/or pen and paper ready for others.

A multiple-choice quiz by AdamM7. Estimated time: 4 mins.

Author
AdamM7

Time
4 mins

Type
Multiple Choice

Quiz #
377,904

Updated
Dec 28 21

# Qns
10

Difficulty
Average

Avg Score
6 / 10

Plays
381

One at a Time - Single Page

Question 1 of 10

1. In a ten question multiple choice (4 options) quiz on FunTrivia, you have a chance of roughly 0.0000954% to get all ten questions right guessing at random. How is this number calculated? Hint

1/(4*10)

(1/4)^10

(4^10)/(10^10)

1/(10^4)

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Question 2 of 10

2. I like Brain Teasers, so I play Brain Twist three days in a row. If the chance that I will 'pass' Brain Twist (by getting at least half of the questions right) is 0.5, what is the chance that I will pass Brain Twist on at least two of those three days? Hint

0.375

0.125

0.5

0.25

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Question 3 of 10

3. Lucky Ducky is a badge awarded to a random user who visits FunTrivia every day. If 100,000 players visit FunTrivia on one day, including myself, what is the chance that I will win the badge? Hint

0.001

0.00001

0.00005

0.0005

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Question 4 of 10

4. The game Word Wizard gives players six possible answers for each question. In a game I play, I am 75% certain that I know the answer to the first question and the second question I guess at random. What is the probability that I have got at least one of these two questions right? Hint

5/8

3/4

19/24

11/12

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Question 5 of 10

5. There's a minibadge called "Zero" awarded to anyone who gets 0/15 in the multiple choice game Obscurity. Each question has four possible options. Guessing all 15 questions at random, what is the chance that I will get every single one of them wrong? Hint

55%

1.3%

0.0007%

13%

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Question 6 of 10

6. Every time I play Piece of Cake I have a 1 in 10 chance of getting the highest score in my set. If I play Piece of Cake seven times, the chance that I will get the highest score in my set at least once is 70%.

True

False

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Question 7 of 10

7. Let's say that the chance of a random person getting over 800 points in Mixed Trivia is 2/5. If someone gets over 800 points in Mixed Trivia, there is a 3/5 chance that they will get over 800 points in Who's the Smartest? What is the chance that a player picked at random will get over 800 points in both games? Hint

8/125

6/25

1/2

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Question 8 of 10

8. There are twenty main categories in which FunTrivia quizzes can be placed (e.g. Animals, Sci/Tech). Assuming that the probability of a quiz going in each category is equally likely, what is the chance that the two newest quizzes on the site will be in the same category? Hint

1/20

1/40

1/400

1/10

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Question 9 of 10

9. In a certain subcategory, the ratio of normal quizzes to photo quizzes is 4:1. What is the chance that a quiz picked at random will be a photo quiz? Hint

0.5

0.25

0.2

0.33

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Question 10 of 10

10. In the Daily Trivia Game, I have a 5% chance of getting 20 out of 20. I have a 15% chance of getting at least 19 questions right and a 10% chance of getting exactly 18 questions right. What is the probability that I will get less than 18/20? Hint

70%

90%

95%

75%

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Quiz Answer Key and Fun Facts

1. In a ten question multiple choice (4 options) quiz on FunTrivia, you have a chance of roughly 0.0000954% to get all ten questions right guessing at random. How is this number calculated?

Answer: (1/4)^10

The chance of getting each question right is 1/4, or 0.25. You multiply these probabilities together to get the probability of getting all of them right: 1/4 * 1/4 * ... * 1/4 = (1/4)^10 = 1/1048576 = 0.000000954 = 0.0000954%

Answer: 0.5

There are eight possible permutations for the three games. Where 'P' means 'pass' and 'F' means 'fail', they are: PPP, PPF, PFP, PFF, FPP, FPF, FFP, FFF.

Since the probability of both passing and failing is equally likely (0.5, or 50%), each of the eight possible options is equally likely. In four of them (PPP, PPF, PFP, FPP), I pass two or three of the games. So the probability that I will pass at least two Brain Twists is 4/8, which can be simplified to a half or 0.5.

3. Lucky Ducky is a badge awarded to a random user who visits FunTrivia every day. If 100,000 players visit FunTrivia on one day, including myself, what is the chance that I will win the badge?

Answer: 0.00001

The chance of any particular player winning is 1/100,000. This is 0.00001 or 0.001%.

Answer: 19/24

The probability of getting at least 1 question right is 1 minus the probability of not getting 1 or more questions right (i.e. getting them both wrong).

The probability of getting both questions wrong is: 25% * 5/6 = 5/24
So the probability of not getting them both wrong is 1 - 5/24, which is 19/24.

Answer: 1.3%

Question 1 was fairly similar, but here we have 15 questions and want to get all of them wrong. The chance of getting one wrong is 3/4, so the chance of getting 15 wrong is (3/4)^15 = 0.013 = 1.3%.

The chance is perhaps surprisingly low, although it's still 14 million times more likely than guessing all 15 right.

Answer: False

Probability is never this simple! You can't just multiply the probability of winning by the number of times you play.

This might become obvious if you think about what would happen if you played 20 games: the probability that you win at least one can't be 200%, because no probability can be greater than 100%.

P(A or B) = P(A) + P(B) - P(A and B)

In words, the probability of getting at least one win is the probability of getting a win on each game added together, minus the probability of winning two or more games. The real formula for seven games is ridiculously complicated, but the basic point is that the probability is not 70% because you have to subtract the probability of winning two or more games.

Answer: 6/25

P(A and B) = P(A) * P(B|A)

This is called conditional probability, and the above formula means "the chance that both statements are true is the probability of the first being true times by the probability of the second being true given that the first is true". Seems complicated, but it's not that hard:

Probability of scoring over 800 in both games = 2/5 * 3/5 = 6/25

Answer: 1/20

The chance that the second quiz will be in the same category as the first is just 1 divided by the number of categories, or 1/20.

Or, going about things the long way, there are 20*20 = 400 different combinations of categories the two quizzes can go in. In 20 of those combinations, the categories of each quiz is the same. 20/400 = 1/20

9. In a certain subcategory, the ratio of normal quizzes to photo quizzes is 4:1. What is the chance that a quiz picked at random will be a photo quiz?

Answer: 0.2

The ratio means that for every four normal quizzes, there is one photo quiz. So out of every five quizzes, one will be a photo quiz: the probability of a random quiz being a photo quiz is one in five, or 0.2.

Or, in numbers: P(Photo) = 1/(1+4) = 1/5 = 0.2.

Answer: 75%

The chance is 1 - 10% - 15% = 75%.

The probability that I will get 20/20 is irrelevant, because it's already included as part of the '15% chance of getting at least 19'. So the chance of getting less than 18 is just the chance that I get 19+ and the chance that I get exactly 18 subtracted from 1.

Source: Author AdamM7

This quiz was reviewed by FunTrivia editor rossian before going online.
Any errors found in FunTrivia content are routinely corrected through our feedback system.

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