# Can you solve the false positive riddle? – Alex Gendler

Mining unobtainium is hard work. The rare mineral appears
in only 1% of rocks in the mine. But your friend Tricky Joe
has something up his sleeve. The unobtainium detector he’s been
perfecting for months is finally ready. The device never fails
to detect unobtainium if any is present. Otherwise, it’s still highly reliable, returning accurate
readings 90% of the time. On his first day trying
it out in the field, the device goes off, and
Joe happily places the rock in his cart. As the two of you head back to camp
where the ore can be examined, Joe makes you an offer: he’ll sell you the ore for just \$200. You know that a piece of unobtanium
that size would easily be worth \$1000, but any other minerals
would be effectively worthless. Should you make the trade? Pause here if you want
to figure it out for yourself. Answer in: 3 Answer in: 2 Answer in: 1 Intuitively, it seems like a good deal. Since the detector
is correct most of the time, shouldn’t you be able
to trust its reading? Unfortunately, no. Here’s why. Imagine the mine
has exactly 1,000 pieces of ore. An unobtainium rarity of 1% means that there are only 10 rocks
with the precious mineral inside. All 10 would set off the detector. But what about the other 990
rocks without unobtainium? Well, 90% of them,
891 rocks, to be exact, won’t set off anything. But 10%, or 99 rocks,
will set off the detector despite not having unobtanium, a result known as a false positive. Why does that matter? Because it means that all in all, 109 rocks will have
triggered the detector. And Joe’s rock could be any one of them, from the 10 that contain the mineral to the 99 that don’t, which means the chances of it containing
unobtainium are 10 out of 109 – about 9%. And paying \$200 for a 9%
chance of getting \$1000 isn’t great odds. So why is this result so unexpected, and why did Joe’s rock seem
like such a sure bet? The key is something called
the base rate fallacy. While we’re focused on the relatively
high accuracy of the detector, our intuition makes us forget to account for how rare the unobtanium
was in the first place. But because the device’s error rate of 10% is still higher than
the mineral’s overall occurrence, any time it goes off is still more likely
to be a false positive than a real finding. This problem is an example
of conditional probability. The answer lies neither in the overall
chance of finding unobtainium, nor the overall chance
of receiving a false positive reading. This kind of background information
that we’re given before anything happens is known as unconditional,
or prior probability. What we’re looking for, though,
is the chance of finding unobtainium once we know that the device did
return a positive reading. This is known as the conditional,
or posterior probability, determined once the possibilities have
been narrowed down through observation. Many people are confused
by the false positive paradox because we have a bias
for focusing on specific information over the more general, especially when immediate decisions
come into play. And while in many cases
it’s better to be safe than sorry, false positives can have
real negative consequences. False positives in medical testing
are preferable to false negatives, but they can still lead to stress or
unnecessary treatment. And false positives in mass surveillance can cause innocent people to be
wrongfully arrested, jailed, or worse. As for this case, the one thing
you can be positive about is that Tricky Joe is trying
to take you for a ride.

## 100 thoughts on “Can you solve the false positive riddle? – Alex Gendler”

1. TED-Ed says:

Sign up for free at https://brilliant.org/TedEd/, and Brilliant will email you the solution to the bonus riddle! Also, the first 833 of you who sign up for a PREMIUM subscription will get 20% off the annual fee. Riddle on, friends!

2. THT Brickfilms says:

Can't you check the rock like, twice?

3. DOGE DOGGIE says:

or joe could scan t multiple times and if it goes off all of those times it's really unobtanium

4. Diamond Yoshi101 says:

Here’s another example of this type of riddle.
You are an Aircraft mechanic in WW2, and the Air Force needs you to reenforce the plane, however, you can only chose one place to reenforce the plane, otherwise the weight will be off and it won’t fly as well. You look and most of them have bullet holes in the tail / rudder, a few have bullet holes in the wings, some have holes at the body, and almost none have holes in the engine. Where do you reenforce the plane? (Answer will be in my reply)

5. Edward ETN says:

I wouldn’t do any trade with a guy named ‘Tricky Joe’

6. Edward ETN says:

You never mentioned a 10% error rate in the beginning!

7. Salty Sweet says:

I don't know much about math, but intuitively I knew these were not good odds. My logic is if the machine can misfire 10% of the time and there's a 1% chance to find unobtanium; it will misfire more than be accurate. If it was 10% and 10% the odds would be better.

8. UPPALA JYOTHIRNAGA VENKATA SATYA PRAKASH says:

Senerio 1

9. Aman Jain says:

finally the first ted ed problem i was able to solve! i used simple conditional probability

10. Nik V says:

In scenario 1 you have one possible pair more than scenario 2

11. Nik V says:

But what if he sold it for 100… Then I personally would buy it, because I have about 1 in 10 chance to get the rock that is worht 1000 (100 x 10). You don't find odds that high anywhere.

12. FreeCoupons 17 says:

The whole time I’m just thinking shoot the rock 10 times then

13. Brieen says:

The real prize is the toxicity you got rid of during the expedition. You don’t need a person like tricky joe you’re better than that

14. Phøtø Bømb says:

Tricky Joe?
I met him in the gang

15. Pablo Verano says:

First riddle I solve

16. Sethmi Karunaratne says:

Is brillant Australian ?

17. Boris Gleichmann says:

I would tell him Id buy it for twice the price if he'd scan the rock 10 more times and the result is the same every 10 times.

18. Irvin Ong says:

Question : Should you buy the Unobtanium?

More like : Should your start thingking like a Crime Investigator and start solving random math and percentages

19. Z Man17 says:

no bc yes makes sence.

EDIT: new it! 😀

20. Sebastian Mena says:

for the bonus, it's quite a riddle, but one thing is certain, there are two queens, a five, and another card if there is the same amount of each card in both scenarios. in scenario 1, they have two queens, and you have a five, the fourth card is what is the problem, it's either a queen, a five, or another overall, making chances about 1/3. in scenario 2, they have the queen and the five, meaning you have one queen, and the extra card is a queen, a five, or another entirely, again making it about 1/3! it doesn't matter which scenario you have, just don't bet stuff because your chances are slim either way

21. tototobi says:

Yay, finally a riddle i solved xD

22. Sakamoto says:

"Nah thanks, I'm a grinder."

23. Absol says:

Say no, because that name alone is a sign that you can’t trust him

24. Alex Ro says:

Lol this is the first riddle I solved on my own:)

25. Uncountable Variety says:

For the bonus riddle, it's Scenario 1 where it's more likely for you to get a pair. Since there are 26 pairs that you can get from the deck (getting each card only once), removing 1 pair only will still leave you with 25 pairs to get (which is Scenario 1), while for Scenario 2, getting 2 different cards will leave only 24 pairs (2 cards won't have a pair).

26. pristine diamond says:

0:06

That's because it's called UNOBTAINium

27. SugaryCherryy says:

Q 5

28. Van Pham says:

Me:notice that the ore is actually plutonium
Me:become a trillionare

29. Ines says:

Woah, i actually solved a riddle right

30. Hanxi Guo says:

I would just buy his machine and copy the materials to make my own machine and shoot the rocks myself x10 times so I can verify. Solved.

31. Y Agent Blueberry says:

Ted ed: Yes, but actually no

32. Michael says:

no! his name is "Tricky Joe"! duh of course he's deceiving you

33. Mr. Black Hole - says:

What if it is 100% gold

34. boo boo kiity f says:

Yeah I did the correct guess

35. Daily Tofu says:

Nah, lets just mine normally, like a human

Sir this is a McDonalds

37. srikanth kusumanchi says:

a pack cards has 13 different cards of 4 shapes each = 52 cards. So u can make 6 pairs with each number card. For ex: with 4 queens u can make 6 pairs (spade&heart, spade&clubs, spade&diamond, heart&clubs, heart&diamond, clubs&diamond). Thus in total there is a probability of 1/78 (6pairs * 13 cards= 78). ur opponent already has 2 queens which means there are only 2 queens left in the remaining deck eliminating 5 pairs of queens above said. that will increase the probability to 1/73 (78-5). In the next scenario ur opponent has 1Queen, 1five. So the number of pairs u can make with remaining cards is 72 pairs (78-3-3). So the probability of getting a pair is better in second scenario which is 1/72 (As we all know that 1/72 is better than 1/73). Like if anyone understand this

38. Fantasy Roleplay says:

People have a habit of looking over specific things, oh you mean the fact that he’s tricky joe or we couldn’t of scanned this twenty time(or maybe it mistakes cause… it gives off a certain pulse or something), or how I’m a poor miner and I don’t have 200% or…. ummmm…. math

39. Pham Nguyen Duc Tin says:

LOL as I work in the Department of Epidemiology, I immediately thought of this as the positive predictive value and gave the instant result :))

40. kevin yang says:

Tricky joe: —> trys it for the first time <— 90% correct
That dude: oh Im not gonna buy that, it’s fake

My thinking was the only 90% accuracy, coupled with the low price would be a scam.

42. Chris Chavez says:

OH MY GOD I ACTUALLY SOLVED SOMETHING!! The first scenario would be the better chance I’m assuming because that only takes away one possible pair out of the deck, the Queens. But with the second scenario, it takes away two possible pairs, queen and a 5 since she has one of each.

43. Lochlan Smith says:

Or you could shoot the device 2 or 3 more times at the rock and there is a SUPER small chance then that you're getting a bad deal, because it ALWAYS detects actual Unobtanium.

44. Drop Beat says:

Want some 90% real water

45. i am a great ape says:

wouldn't you still be checking 90% less rocks? so instead of unobtanium being 1 percent of the rocks you carry its about 9%, isn't it a reusable tool? it would still greatly increase the chances of you finding unobtanium.

46. its the spiffy says:

Jo mama

47. Spacciacc says:

This was the easiest

48. Elefant /Ferdinand says:

"And paying \$200 for a 9% chancr of getting \$1000 isnt great odds"

You boys ever heard of the lottery?

49. Hyper 17 says:

Who’s joe

50. Emma Payne says:

I did the math and ther is a higher chance o get a double if you’r friend has two queens

51. Crimson twelve says:

If Ik the ore is in 10% or rocks and the size of the rock if it was pure would be \$1,000 at best odds that’s still only \$100 of ore plus the cost of labor on me! That alone is enough to sway me away, plus given the ore could have been picked up from another sample I would have him retest it a few times outside to make the probability that it is in there higher. if positive best I would give him is \$50

52. NNNK MK says:

Soooo, ya sayin’ diamonds, obsidian, emerald, sapphire, aquamarine, opal and all the other precious rocks are worthless???

53. corny cornrows says:

Joe mama

54. Nafissa Wahab says:

i thought unobtainium was fake…

55. Aren Bedros says:

Who’s joe

56. Nicolas Mobley says:

Scenario 1

57. akgamer182 says:

Shoot it with the gun again

58. Mohammed Barwani says:

Alright good riddle but who is joe?

59. Gunning Analyst of NBA says:

This is kinda like a more expensive lottery

60. Amelia Ring says:

1

61. Yggy Faeldo says:

What if you press the first one thrice?

62. Medicine91 says:

Simple, use Bayes

63. Amir Allon says:

In the first time I watched the video, i didn't understand that tricky joe sell the ore to me. You should say that

64. Sara Rayhan says:

I hope Tricky Joe isn't a nickname

65. Amitie says:

So gold would be effectively worthless.

66. Dusty Rhodes says:

Another probability equation disguised as a riddle. Do something different for once.

67. Rex17 Ly says:

This is the only riddle I could solve 🙂

68. black roses also bloom says:

69. Dahyun's extraness says:

you know who taught joe how to be tricky?

joe mama

70. Pink Shep says:

Yay a riddle I finally got right

71. Mary Sebastian says:

Him: so why did joes rock seem such a great bet
Me: it because they eat too many dum dum’s

72. YellowMarkers says:

This is honestly easier than the passcode riddle. Its so intuitive. I didnt even need to think to solve this, and i got it right.

73. ekimmak says:

It's weird, because my immediate mathematics tells me "it's only worth it if it's a \$20 price tag", and I can't remember what those mathematics are after seeing the video.

This make no sense you said the laser gun could find unobtanium without failure but then you said it would have a nine percent chance of it finding it

75. Faith Corral says:

Amy is not my friend

76. Imnotaweeb says:

This is my first time getting a riddle right since watching this channel

77. Fox Art says:

Can you-

NO I CANT OK

but I’ll still watch

78. Seth says:

Just use it on the rock again

79. Entity Valkyrie 2 - Fixing Your Flags version 2 says:

Only put it in cart if it returned a positive reading four consecutive times — that increases the accuracy from 90% to 99.99%

80. Budgie Birb says:

It’s called unobtainium or however you spell it, you can’t obtain it.

81. Cj Cola says:

Nooooooooooooooooo!

82. Matthew Yao says:

Who's Joe?

83. Jericho Loyola says:

2:26 , because I'm not good in English

84. Mary Elliot says:

I ACTUALLY SOLVED THIS ONE

(after watching about 30 of the other ones)

85. Andy Pang says:

Just use the detector 2 times

86. Annabeth Chase says:

then it turns out it is unobtainian

87. Color Code says:

Tricky joe we're not friends anymore

88. The one who sucks says:

Everytime I hear “fallacy” I think of the word “phallus”

89. ErzieWerzie :3 says:

You could just use the detector multiple times on the same ore.

90. Katie lu says:

I would automatically know it's not worth it cuz the guy's name is literally tricky Joe. Major clue u-u

woah- this is so genius im just- wOah.

92. Mausmi Sharma says:

93. Hans Farrel says:

Just scan the rocks twice

94. Ace_Houndz says:

Tricky joe- you know who i am?
Me-no,who are you?
Tricky joe- i am joe
Me-wait,who is joe?
Tricky joe- JOE ROCK

brought to you by: joe mama jokes co.

95. Mirrored {} Chaos says:

HOWEVER…. joe was offering 200\$ when its supposed to be worth 1000\$
as logic would indicate joe is possibly scamming you because he knows that the rock is worthless.

96. Grace Johnson says:

I wouldn’t be friends with trickery joe but…

97. Katanyuf says:

Plot twist: tricky joe was right and is now a millionare

98. some random commenter you found says:

Would joes rock technically not be worth 800 cuz youre paying 200 dollars for something possibly worth 1000

99. LITTLE ROCK says:

This is the exact reason that urine tests are so unreliable. When they say that it is accurate 97% of the time, they do not take into account the false positives and the false negatives in their tests.

100. 전유범 says:

I,s so bom!