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# A Matter of Probability... Trivia Quiz

### Nothing is certain in this quiz. Test your calculation of probability. The questions are tricky, but can all be solved by logical thinking and a little bit of mathematics. E.g. a probability of 1/4 means one chance out of four, or 25%.

A multiple-choice quiz by queenofsheba. Estimated time: 5 mins.

Author
queenofsheba
Time
5 mins
Type
Multiple Choice
Quiz #
280,045
Updated
Dec 03 21
# Qns
10
Difficulty
Tough
Avg Score
5 / 10
Plays
1477
Awards
Top 35% Quiz
This quiz has 2 formats: you can play it as a or as shown below.
Scroll down to the bottom for the answer key.
1. You pick two cards out of a standard pack of 52. The first card is a king. What's the probability of the second card also being a king? Hint

1/13
1/14
3/13
1/17

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2. You toss a coin four times. The first, second and third toss are heads. What's the probability of the fourth toss also being heads? Hint

1/2
1/8
1/4
1/16

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3. I choose two different numbers between 1 and 10 (1 and 10 are included). You try to guess the two numbers, in any order. How much chance do you have to guess both numbers correctly in one attempt? Hint

1/90
1/45
1/100
1/25

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4. We're playing poker with a standard pack of fifty-two cards without jokers. You have two pairs: 3, 3, 4, 4, 8. You are unaware of which cards the other players are holding. You decide to replace the 8 by another card from the pack. How do you rate your chances to turn your hand into a full house? (Full house means one trio and one pair.) Hint

1/13
4/47
2/13
1/26

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5. Ashley throws two normal, six-faced dice. How much chance does she have for a total of at least 11? Hint

1/12
1/18
2/11
1/6

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6. Eight cardboard boxes are standing on the table. Two among them contain a present, the other six are empty. You are allowed to open two boxes. How much chance do you have to find at least one present? Hint

7/16
9/16
15/28
13/28

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7. Peter, Mark, Anne and Rose are four good friends. They belong to a group of sixty pupils who are to be divided at random into three classes of twenty. What's the probability of all four friends sharing the same class? Hint

1/81
19x18x17/59x58x57
1/64
1/12

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8. I have thirty socks in total disorder in my closet. Ten are black, ten are red and ten are brown, but I can't distinguish the colours in the dark. How many socks do I have to take to be sure of having at least one pair of the same colour? Hint

12
11
4
3

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9. There are seven cups of tea. Two among them contain a deadly poison that acts within an hour. You and I both drink one cup simultaneously. How big is the chance that we both survive? Hint

10/21
25/49
11/21
24/49

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10. If someone answers these ten multiple choice questions, all with four options, totally at random, what is the chance that he has all answers wrong? Hint

59,049/1,048,576
1/1,024
1/1,048,576
243/1,024

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Quiz Answer Key and Fun Facts
1. You pick two cards out of a standard pack of 52. The first card is a king. What's the probability of the second card also being a king?

There are fifty-one cards left. Three of those are a king, so you have three chances out of fifty-one, which equals one out of seventeen.
2. You toss a coin four times. The first, second and third toss are heads. What's the probability of the fourth toss also being heads?

The result of the first three tosses doesn't influence the fourth. The odds between heads and tails are always even.
3. I choose two different numbers between 1 and 10 (1 and 10 are included). You try to guess the two numbers, in any order. How much chance do you have to guess both numbers correctly in one attempt?

You have two chances out of ten to guess the first number, or 1/5. Only one of the remaining nine is correct, so you have one chance out of nine to guess that one too. 1/5 x 1/9 = 1/45.
4. We're playing poker with a standard pack of fifty-two cards without jokers. You have two pairs: 3, 3, 4, 4, 8. You are unaware of which cards the other players are holding. You decide to replace the 8 by another card from the pack. How do you rate your chances to turn your hand into a full house? (Full house means one trio and one pair.)

You need to pick a 3 or a 4. There are two 3's and two 4's left among the remaining forty-seven cards, so four cards out of forty-seven can give you a full house. It doesn't matter which five cards I have. There are 47 unknown cards to you, no matter if the 3's and 4's are in the pack or in someone else's hands.
5. Ashley throws two normal, six-faced dice. How much chance does she have for a total of at least 11?

You can throw thirty-six possible combinations with two dice (6x6). Three of those give a sum of at least 11: 5+6; 6+5 and 6+6. The probability of throwing at least 11 is 3/36, or 1/12.
6. Eight cardboard boxes are standing on the table. Two among them contain a present, the other six are empty. You are allowed to open two boxes. How much chance do you have to find at least one present?

You can calculate the probability of picking two empty boxes. If you pick one box, you have a chance of 6/8 (=3/4) to find nothing inside. Then there are seven boxes left, of which five are empty, so there's a chance of 5/7 that your second box is empty as well. 3/4 x 5/7 = 15/28 to find nothing, which means 13/28 to find at least one present.
7. Peter, Mark, Anne and Rose are four good friends. They belong to a group of sixty pupils who are to be divided at random into three classes of twenty. What's the probability of all four friends sharing the same class?

Mark has a 19/59 chance to be in the same class as Peter. Anne has an 18/58 chance to be in the same class as the first two, and Rose has a 17/57 chance to be in the same class as the other three.
8. I have thirty socks in total disorder in my closet. Ten are black, ten are red and ten are brown, but I can't distinguish the colours in the dark. How many socks do I have to take to be sure of having at least one pair of the same colour?

There are three colours, so if I only take three socks they can all have a different colour. As soon as I take a fourth one they can't all be different.
9. There are seven cups of tea. Two among them contain a deadly poison that acts within an hour. You and I both drink one cup simultaneously. How big is the chance that we both survive?