Monkey Math Challenge?

Question

I doubt there are any mathematicians out there, but what is the probability of a monkey typing a 100 page science fiction novel on the first try if you allowed it to bang on a typewriter? Assume that there are 2000 characters per page, 46 keys on a keyboard (one for each letter, number and punctuation mark) and for simplicity's sake that all keys are equally likely. There are no shift bars or capital letters on this keyboard.

Good luck!

This is not my homework. I just want to know how to calculate this sort of thing, and am curious about the answer.

Answer 1

You said a "100 page science fiction novel "

let's assume you mean there IS a particular a 100 page science fiction novel and the probability of the monkey typing it.

the total characters in the novel is 100*2000 = 200000

Now for each character, the probability of matching the exact character is 1/46

So the probability of typing the entire novel is
(1/46)^200000

Well, the interesting part is that it is not zero. So buy a monkey and give it a key board if you like.

Answer 2

The probability is clearly minute. Since you've simplified, I'll add a simplification of my own. Non-standard English is out, and words must be used throughout in normal fashion. This leaves out, for example, starting the first page with (*&)(* (a la Harlan Ellison possibly).

So, for the first letter of the first word, there is only a probability of 26/46 of a useful random hit, assuming even that, for example, "zounds!" or "xylophones" would be a good first word.

Now the second letter of the first word is much more limited. If the first letter was a vowel, only a few words can continue with another vowel, while if the first letter was a consonant, the second letter much more often is a vowel. The probability of a useful second letter is thus only a fraction of the 26/46 first letter probability, and since both letters are needed, the combination of two useful letters in a row has a probability of <(26/46)*(26/46) or less than 0.32.

For an average 5-letter word, then, the probability of hitting useful keys by random is <(26/46)^5 or about 0.05. If we've got a word, and additional letters will not make a word, a space or punctuation mark must be hit, but there are only comma, period, exclamation point, perhaps a dash or semicolon, let's say 8 possible useful keys, so the probability is further reduced by multiplying 0.05 times 8/46, and we are down below 1% (0.008).

This is roughly how it would be done and it estimates the probability high. Analysis with letter and word frequency will not permit 26/46 for each letter, but would sum the 2- letter sequences based on the said frequencies, netting far less than 31% for useful 2-letter combinations.

Here's one more simplification that gives a very high probability estimate that's still so small that the full outcome you've proposed is impossible: Suppose all the monkey has to do for the first page is do some stream of consciousness monolog without punctuation, consisting of one word repeated for the whole first page: damn damn damn damn damn (he's clearly disappointed) damn damn damn OR help help help help...

The monkey has to hit the same key every fifth bang. Way too improbable for a 2000 character page, with 400 words and 400 spaces.

So how about the simplest possible first page, one letter repeated the whole 2000 characters. No, that's out, with a probability of (26/46)^2000.

I'm glad it's not your homework. A detailed answer would give your department chairman a migraine!

Answer 3

Not only would this monkey have to be typing words, but the words would need to relate to each other to form a story. It would be just as likely that the monkey would type the first 100 pages of War and Peace since it would all just be blind luck. Let's start by trying to figure out the chances of the monkey starting out with the two words "once upon" The chances of it hitting the o is 1 out of 46. the chance of it next hitting an "n" is 1 out of 46, and so on, which makes the odds of randomly typing "once upon"= to 46x46x46x46x46x46x46x46x46 (we need to include the space as well) or a one out of 922190162669056 ( 46 to the ninth power) If we extend this to the entire 100 pages then it would equal 46 to the 200,000th power which is so large that it is probably a larger number than the number of atoms from all the matter in the known universe. Not bloody likely.

Answer 4

Okay, the number of characters the monkey has to type is 200000 in total, and in the right order. Each character has a 1/46 shot at coming up, and since the characters have to be in a certain order, I think you have to multiply 1/46 by 1/46 200000 times, so 1/46^200000. In other words, don't hold your breath waiting for that novel.

Answer 5

for each character on each page, there are 46 possibilities...
46*2000*100=9200000

so 1 in 9,200,000 or .000000108
not good odds, though better than winning the powerball (1 in 150 million)

Answer 6

Yee, Good luck to you!