# PROBABILITY RIDDLES

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## Die Toss Riddle

Hint:
One in six. A die has no memory of what it last showed.
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Solved: 76%

## The Traffic Light Riddle

Hint:
The probability of the driver encountering a yellow light and the light turning red before the car enters the intersection is about 5.5%.

At 45 mph the car is traveling at 66 feet/second and will take just over 3 seconds (3.03) to travel the 200 feet to the intersection. Any yellow light that is in the last 3.03 seconds of the light will cause the driver to run a red light.

The entire cycle of the light is 55 seconds. 3.03/55 = 5.5%.
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Solved: 45%

## The Prime Number Riddle

Hint: Remember that 1 is not a prime number.
Those that remain behind must have written {1,4,6,8,9} and from this only {1,9} are odd. The probability of an odd number is thus 2/5.
Expected number of odds is 2/5 * 90 = 36
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## Russian Roulette Riddle

Hint:
Russian Roulette
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

Puzzle ID: #17681
Fun: *** (2.59)
Difficulty: ** (2.07)
Category: Probability
Submitted By: JMCLEOD****
Corrected By: cnmne

You are in a game of Russian Roulette with a revolver that has 3 bullets placed in three consecutive chambers. The cylinder of the gun will be spun once at the beginning of the game. Then, the gun will be passed between two players until it fires. Would you prefer to go first or second?

Label the chambers 1 through 6. Chambers 1 through 3 have bullets and chambers 4 through 6 are empty. After you spin the cylinder there are six possible outcomes:

1. Chamber 1 is fired first: Player 1 loses
2. Chamber 2 is fired first: Player 1 loses
3. Chamber 3 is fired first: Player 1 loses
4. Chamber 4 is fired first: Player 2 loses (First shot, player 1, chamber 4 empty. Second shot player 2, chamber 5, empty. Third shot player 1, chamber 6 empty. Fourth shot player 2, chamber 1 not empty.)
5. Chamber 5 is fired first: Player 1 loses (First shot, player 1, chamber 5 empty. Second shot player 2, chamber 6, empty. Third shot player 1, chamber 1 not empty.)
6. Chamber 6 is fired first: Player 2 loses (First shot, player 1, chamber 6 empty. Second shot, player 2, chamber 1, not empty)

Therefore player 2 has an 4/6 or 2/3 chance of winning.
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Solved: 69%

## Blue Eyes Riddle

Hint: Given my brother's blue eyes, what are the odds on my pair of eye-color genes?
1 in 3.

Since my brother has blue eyes (bb), both of my parents carry one brown and one blue gene (Bb). The three possibilities for my genotype, equally likely, are BB, Bb, and bB. Thus, there is a 2/3 chance that I carry a blue gene.

If I carry a blue gene, there is a 50% chance I will pass it on to my first child (and, obviously, 0% if I carry two brown genes).
Since my child will certainly get a blue gene from my wife, my gene will determine the eye color.

Multiplying the probabilities of those two independent events, there is a chance of 1/2 x 2/3 = 1/3 of my passing on a blue gene.
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## The Coin Toss Riddle

Hint: Think what would be most likely to happen if you chose HHH, would this be a good decision?
The answer is to let your friend go first. This puzzle is based on an old game/scam called Penny Ante. No matter what you picked, your friend would be able to come up with a combination which would be more likely to beat yours. For example, if you were to choose HHH, then unless HHH was the first combination to come up you would eventually lose since as soon as a Tails came up, the combination THH would inevitably come up before HHH. The basic formula you can use for working out which combination you should choose is as follows. Simply take his combination (eg. HHT) take the last term in his combination, put it at the front (in this case making THH) and your combination will be more likely to come up first. Try it on your friends!
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## The Cheap Mp3 Player

Hint:
With only 6 tracks on the player:
The first chapter has been set to play first. The probability of the next 5 chapters playing in order is 1/5! = 1/120.

With the music on the player as well:
Seeing as I don't care about when the music plays, it doesn't change anything. The answer is still 1/120.
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Solved: 49%

## The 3 Inch Cube Riddle

Hint: Visualize the core of the cube.
ZERO.

The core of the 3 inch cube when cut, has all faces that are not painted. Hence at least one cube with no painted face always occurs.
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## Yahtzee Riddle

Hint: Think of the probability of NOT getting a full house.
5/9

The answer is NOT 2/3 because you cannot add probabilities. On each roll, the probability of getting a 2 or a 4 is 1/3, so therefore, the probability of not getting a 2 or a 4 is 2/3. Since the die is being rolled twice, square 2/3 to get a 4/9 probability of NOT getting a full house in two rolls. The probability of getting a full house is therefore 1 - 4/9, or 5/9.
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## The Secret Santa Exchange

Hint: It's not as difficult as it seems. It's the number of ways the friends can form a circle divided by the number of ways the names can be drawn out of the hat.
1/10

For a group of n friends, there are n! (n factorial) ways to draw the names out of the hat. Since a circle does not have a beginning and end, choose one person as the beginning and end of the circle. There are now (n-1)! ways to distribute the remaining people around the circle. Thus the probability of forming a single circle is

(n-1)! / n!

Since n! = (n-1)! * n (for n > 1), this can be rewritten as

(n-1)! / (n*(n-1)!)

Factoring out the (n-1)! from the numerator and denominator leaves

1/n

as the probability.
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## 100 Blank Cards Riddle

Hint: Perhaps thinking in terms of one deck is the wrong approach.
Yes!

A sample strategy:
Divide the deck in half and turn over all lower 50 cards, setting aside the highest number you find. Then turn over the other 50 cards, one by one, until you reach a number that is higher than the card you set aside: this is your chosen "high card."

Now, there is a 50% chance that the highest card is contained in the top 50 cards (it is or it isn't), and a 50% chance that the second-highest card is contained in the lower 50. Combining the probabilities, you have a 25% chance of constructing the above situation (in which you win every time).

This means that you'll lose three out of four games, but for every four games played, you pay \$40 while you win one game and \$50. Your net profit every four games is \$10.

Obviously, you have to have at least \$40 to start in order to apply this strategy effectively.
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## Little Billy's Calculator

Hint: Think about how many ways he could possibly get 6.
There is a 4% chance.

There are 16 possible ways to get 6.

0+6
1+5
2+4
3+3
6+0
5+1
4+2
9-3
8-2
7-1
6-0
1x6
2x3
6x1
3x2
6/1

There are 400 possible button combinations.

When Billy presses any number key, there are 10 possibilities; when he presses any operation key, there are 4 possibilities.

10(1st#)x4(Operation)x10(2nd#)=400

16 working combinations/400 possible combinations= .04 or 4%
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## The Blue And Red Dice Riddle

Hint:
Each die has 6 faces. When two dice are thrown, there are 36 equally possible results. For chances to be even, there must be 18 ways of getting the same color on top. Let X be the number of red faces on the second die. We have: 18 = 5X + 1(6 - X)

X = 3

The second die must have 3 red faces and 3 blue faces.
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Solved: 60%

## The Gardners Riddle

Hint:
Gretchen said that there were 4 girls in the family, three of whom were blond.

This would make the probability that she saw two blonds (3/4) * (2/3), which equals 1/2.

Other numbers would work, but the next pair would lead to a rather large family.
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Solved: 76%
Hint: Their dad is a very smart person.
Believe it or not, both Mike and James have a 1/2 chance of winning.

James wins if:
-he calls both coin flips right = 1/2 x 1/2 = 1/4
OR
-he does not call both coin flips right, Mike does not call the die roll correctly, and he guesses the number on the spinner right = 3/4 x 5/6 x 2/5 = 30/120 = 1/4

1/4 + 1/4 = 1/2

Mike wins if:
-James does not call both coin flips right and he calls the die roll correctly = 3/4 x 1/6 = 3/24 = 1/8
OR
-James does not call both coin flips right, he does not call the die roll correctly, and Mike does not guess the number on the spinner right = 3/4 x 5/6 x 3/5 = 45/120 = 3/8

1/8 + 3/8 = 1/2

Of course, dad could have just flipped a coin
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## Post Your Probability Riddles Puns Below

Can you come up with a cool, funny or clever Probability Riddles of your own? Post it below (without the answer) to see if you can stump our users.

1. What do you call a probability that's always wrong? An improbability!

2. Why did the probability feel depressed? It couldn't find its half!

3. How do you tell the difference between probability and statistics? Probability has a chance of being right!

4. Why are probability and statistics such good friends? They're always talking about the standard deviation!

5. How did the probability know it was going to rain? It had a 50% chance!

6. What do you call a group of probabilities that can't agree? A dispersed distribution!

7. Why did the probability skip the party? It didn't have a standard deviation outfit!

8. Why did the geometry teacher laugh at the probability question? It was such a trig-gy one!

9. What did the probability say when it saw a pie chart? "I can't wait to see the data slice!"

10. Why are probabilities and puns alike? They both have a chance of being groan-worthy.

11. Why did the probability party get out of hand? The drinks were distributed randomly!

12. Why won't anyone invite the probability to play darts? It always hits outside the standard deviation!

13. How did the probability know it was in trouble? It saw the confidence interval closing in!

14. Why did the probability go to the casino? To calculate the odds of winning, of course!

15. How did the probability know it was time to pay the rent? The bell curve told it so!

16. What did the probability say to the statistician in a bad mood? "Looks like someone needs a little bit of normality!"

17. Why did the probability become a politician? It knew how to spin the odds in its favor!

18. How did the probability know it was time to go to the gym? The odds of getting in shape were greater than the odds of staying out of shape!

19. What do you call a probability with a gambling problem? A casino's best friend!

20. Why did the probability go to the grocery store? It wanted to calculate the chances of a foodborne illness!

21. How did the probability know it was time to eat veggies? The odds of staying healthy were too good to pass up!

22. What did the probability say to the gambler? "Roll the dice and let's see where the chips fall!"

23. Why did the probability become a weather forecaster? It knew how to predict the odds of a sunny or rainy day!

24. How did the probability know it was time to invest? It saw the trend line going up and the risk going down!

25. What did the probability say to the stockbroker? "Buy low and sell high because there's always a chance of making money!"

26. Why did the probability go bungee jumping? To calculate the risk of falling and the likelihood of surviving!

27. How did the probability know it was time to get a flu shot? The odds of avoiding the flu were greater than the odds of getting sick!

28. What do you call a probability with trust issues? A skeptical distribution!

29. Why did the probability go to the optometrist? To calculate the odds of needing glasses!

30. How did the probability know it was time to get a pet? The probability of happiness was too good to ignore!

31. Why did the probability become a scuba diver? It knew how to calculate the odds of nitrogen bubbles forming!

32. How did the probability know it was time to do laundry? The odds of having clean clothes were too good to pass up!

33. What did the probability say to the mathematician who didn't like probability puns? "What are the odds of you laughing at one of my jokes?"

34. Why did the probability become a chef? It knew how to calculate the ingredients' proportions and the chances of a tasty dish!

35. How did the probability know it was time to go to sleep? The odds of waking up refreshed were greater than the odds of staying up late!

36. What do you call a probability with low self-esteem? A confidence interval!

37. Why did the probability go to the dance club? To calculate the chances of finding a soulmate!

38. How did the probability know it was time to get a new car? The chances of a breakdown were too high to ignore!

39. Why did the probability become a scientist? It knew how to calculate the odds of a breakthrough discovery!

40. How did the probability know it was time to stop procrastinating? The chances of success were greater with action than without!

41. What did the probability say to the psychiatrist? "I'm having second thoughts about being a statistic!"

42. Why did the probability go to the amusement park? To calculate the odds of having fun on each ride!

43. How did the probability know it was time to take a vacation? The odds of getting burnt out were too high to ignore!

44. What do you call a probability that's always indecisive? A probability cloud!

45. Why did the probability become a pilot? It knew how to calculate the odds of turbulence and safety!

46. How did the probability know it was time to quit smoking? The chances of a healthy lifestyle were too good to pass up!

47. What did the probability say to the insurance adjuster? "I hope the risk of an accident is not too high!"

48. Why did the probability become a teacher? It knew how to calculate the odds of student engagement and learning!

49. How did the probability know it was time to buy a house? The odds of stability and comfort were higher with property than with renting!

50. Why did the probability become a time traveler? It knew how to calculate the odds of changing history!