One In A Googol vs One In A Googolplex

David Sklansky · #1 05-19-2007, 02:00 AM

I've often toyed with having a bit of fun with these two numbers as it applies to probability questions especially since it was my father's math professor who coined those words. A googol is ten to the hundredth power. In other words one followed by one hundred zeroes. A googolplex is ten to the googleth power. One followed by a googol zeroes.

I am going to periodically start a thread asking about the probability of extremely unlikely events. In each case I will ask which of three categories the answer is:

A. More common than one/googol.

B. Rarer than one in a googol but more common than one in a googolplex.

C. Rarer than one/googolplex.

THESE QUESTIONS ARE ONLY DIRECTED TOWARD THOSE WHO ARE NOT GOOD AT MATH. If you are, you will spoil the fun by answering them. In fact it won't be fun if even the math challenged try to calculate the answer. Better they just give their gut feelings.

A, B, or C?

1. The chances that you will win the next 100 lotteries in a row.

2. The chances that a specific player will hit 500 homeruns this year, assuming everything is random and he normally hits 10.

3. Your 90 year old grandmother's next 50 bowling games are 300.

4. Every single time a poker machine is played for the next million years it will deal a pat Royal Flush.

5. Your pet parrot, who has been taught to randomly speak every individual sound in the English language, randomly recites Hamlet.

6. All players who are capable of reaching the cup from outside the green always sink their chip or drive and never have to put again for the next 50 years.

I mean for all these questions to be pure probability questions regarding multiple independent events with no funny business or divine intervention going on. I think even the most ardent atheist would admit that if any of these things happened it would more likely be the work of a designer than a miniscule underdog coming in randomly. But for the purpose of these questions we assume that isn't happenning.

SNOWBALL · #2 05-19-2007, 02:12 AM

[ QUOTE ]
1. The chances that you will win the next 100 lotteries in a row.

[/ QUOTE ]

b

[ QUOTE ]
2. The chances that a specific player will hit 300 homeruns this year, assuming everything is random and he normally hits 10

[/ QUOTE ]

A

[ QUOTE ]
3. Your 90 year old grandmother's next 50 bowling games are 300.

[/ QUOTE ]

B

[ QUOTE ]
4. Every single time a poker machine is played for the next million years it will deal a pat Royal Flush.

[/ QUOTE ]

C

[ QUOTE ]
5. Your pet parrot, who has been taught to randomly speak every individual sound in the English language, randomly recites Hamlet.

[/ QUOTE ]

C

[ QUOTE ]
6. All players who are capable of reaching the cup from outside the green always sink their chip or drive and never have to put again for the next 50 years.

[/ QUOTE ]

C

yNnOs · #3 05-19-2007, 02:14 AM

1. B
2. A
3. A
4. C.
5. B.
6. B.

I hope you were only expecting answers and not explanations. Though I'm good at math, I'm not the best with probability.

soon2bepro · #4 05-19-2007, 02:29 AM

Alright, gut only. And I'm not good at math. I already have a hard time imagining these numbers in my head.

[ QUOTE ]

1. The chances that you will win the next 100 lotteries in a row.

[/ QUOTE ]

B

[ QUOTE ]

2. The chances that a specific player will hit 300 homeruns this year, assuming everything is random and he normally hits 10

[/ QUOTE ]

A

[ QUOTE ]

3. Your 90 year old grandmother's next 50 bowling games are 300.

[/ QUOTE ]

That would depend on her physical ability and experience in bowling, but I'd say A

[ QUOTE ]

4. Every single time a poker machine is played for the next million years it will deal a pat Royal Flush.

[/ QUOTE ]

definitely C, unless it's not in constant use, which is really not the point here I presume

[ QUOTE ]

5. Your pet parrot, who has been taught to randomly speak every individual sound in the English language, randomly recites Hamlet.

[/ QUOTE ]

C

[ QUOTE ]
I think even the most ardent atheist would admit that if any of these things happened it would more likely be the work of a designer than a miniscule underdog coming in randomly.

[/ QUOTE ]

Not at all. If you could predict it somehow, then we could discuss the matter, but up front, just because an extremely unlikely event happens doesn't mean anything.

Sephus · #5 05-19-2007, 03:09 AM

seems like people are overusing C.

soon2bepro · #6 05-19-2007, 05:08 AM

[ QUOTE ]
seems like people are overusing C.

[/ QUOTE ]

really?



According to Wikipedia, Hamlet consists of 29,551 words, and the bird can't screw up in one. How many different words are in the english language anyway? I just googled these up:

"The Second Edition of the Oxford English Dictionary contains full entries for 171,476 words in current use, and 47,156 obsolete words. To this may be added around 9,500 derivative words included as subentries"

"But estimates of Shakespeare’s vocabulary vary from about 18,000 to 25,000 in various books, because writers have different views about what constitutes a distinct word."

And David didn't even say the parrot knew all the words, but all the sounds, which makes it extremely more unlikely.

I don't know how many tries the parrot gets, but even in a lifetime of tries, C seems extremely optimistic. There's just no way it'll get it right.

A pat royal is like, what, one in 500,000 or something? (quick google didn't help, too many promotions and bragging) In my original reply I thought it was just one particular machine, now I saw it's every video poker machine?... Get out of here!`

Sephus · #7 05-19-2007, 01:41 PM

[ QUOTE ]
[ QUOTE ]
seems like people are overusing C.

[/ QUOTE ]

really?



According to Wikipedia, Hamlet consists of 29,551 words, and the bird can't screw up in one. How many different words are in the english language anyway? I just googled these up:

"The Second Edition of the Oxford English Dictionary contains full entries for 171,476 words in current use, and 47,156 obsolete words. To this may be added around 9,500 derivative words included as subentries"

"But estimates of Shakespeare’s vocabulary vary from about 18,000 to 25,000 in various books, because writers have different views about what constitutes a distinct word."

And David didn't even say the parrot knew all the words, but all the sounds, which makes it extremely more unlikely.

I don't know how many tries the parrot gets, but even in a lifetime of tries, C seems extremely optimistic. There's just no way it'll get it right.

A pat royal is like, what, one in 500,000 or something? (quick google didn't help, too many promotions and bragging) In my original reply I thought it was just one particular machine, now I saw it's every video poker machine?... Get out of here!`



[/ QUOTE ]

calculationish stuff in white 

you can do the halmet problem by assuming (conservatively) 100 different english sounds and 300,000 sounds in the play. seems like slam dunk to me.

if a pat royal is even one in a million and you need it to be dealt a quintillion times in a row (a trillion times a year for a million years), don't you end up with like 6 quintillion zeros? you don't even get close to C.

soon2bepro · #8 05-20-2007, 01:05 AM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
seems like people are overusing C.

[/ QUOTE ]

really?



According to Wikipedia, Hamlet consists of 29,551 words, and the bird can't screw up in one. How many different words are in the english language anyway? I just googled these up:

"The Second Edition of the Oxford English Dictionary contains full entries for 171,476 words in current use, and 47,156 obsolete words. To this may be added around 9,500 derivative words included as subentries"

"But estimates of Shakespeare’s vocabulary vary from about 18,000 to 25,000 in various books, because writers have different views about what constitutes a distinct word."

And David didn't even say the parrot knew all the words, but all the sounds, which makes it extremely more unlikely.

I don't know how many tries the parrot gets, but even in a lifetime of tries, C seems extremely optimistic. There's just no way it'll get it right.

A pat royal is like, what, one in 500,000 or something? (quick google didn't help, too many promotions and bragging) In my original reply I thought it was just one particular machine, now I saw it's every video poker machine?... Get out of here!`



[/ QUOTE ]

calculationish stuff in white 

you can do the halmet problem by assuming (conservatively) 100 different english sounds and 300,000 sounds in the play. seems like slam dunk to me.

if a pat royal is even one in a million and you need it to be dealt a quintillion times in a row (a trillion times a year for a million years), don't you end up with like 6 quintillion zeros? you don't even get close to C.


[/ QUOTE ]

 Wait, how can it be easier to get all the sounds right than all the words right? Since there are so many sound combinations that don't make a real word, it ought to be easier if the parrot just knew all the words.

And as I said I'm not good at math, but it seems like you're making a mistake in your pat royal calculations? Someone please confirm

PairTheBoard · #9 05-20-2007, 01:24 AM

[ QUOTE ]
calculationish stuff in white

 you can do the halmet problem by assuming (conservatively) 100 different english sounds and 300,000 sounds in the play. seems like slam dunk to me. 

[/ QUOTE ]

White:


(100)^300,000 = (10^2)^300,000 = 10^600,000 < 10^1,000,000

That's 10^(1 followed by 6 zeros)

Compare to C



PairTheBoard

PairTheBoard · #10 05-19-2007, 03:11 AM

[ QUOTE ]
I think even the most ardent atheist would admit that if any of these things happened it would more likely be the work of a designer than a miniscule underdog coming in randomly. But for the purpose of these questions we assume that isn't happenning.

[/ QUOTE ]

I scientist would begin work looking for yet to be discovered laws of physics to explain the anomaly.

PairTheBoard