Help solving this. I'll appritiate explanation.?

Question

It has been said that an army of dedicated monkeys, typing at random, would eventually produce all of Shakespeare’s works. How long, on average, would it take 1 million monkeys, each typing on a 46-key typewriter (space included but no shift key) at the rate of one key stroke per second, to type the phrase “to be or not to be”?

Thanks harry, but you know...I'm a little dumb! Will you please explain how did you convert the probability into time. I mean if there is a prob. of 1/x then what will be the time needed on average?

Answer 1

ok, so the probablility for one monkey is 1/46^18 that is the probability that the keys are typed in sequence.

1 / 850434696123579966501779931136
or
1.1758692402346271614032682375194e-30

so for a million monkeys....

1,000,000 / 850434696123579966501779931136
or
1.1758692402346271614032682375194 e-24

so if i understand this right,

one hell of a long time.

1175869240234627161403268 and a quarter seconds

37286569007947335 ish years


...


on average.

except, you could use the government trained supermonkeys, who write most of the press releases, and probably write their own great plays in their spare time. whilst sitting by the fire in the evening with a pipe and slippers.



edit:

ok, so actually i didn't think about the time. ignore the above.

lets see, one letter, has a probability of 1 in 46, so out of 46 times, we could take the average as 23. thats 23 seconds for one monkey to type one letter your waiting for on average, because on average, the letter you want will be the 23rd typed. and you specified one keystroke per second.

2 letters together, in sequence, the probability is 1/46^2,
or 1 in 2116 so again, 2116 seconds to get a probability of one. with the average being the middle, or 1058 seconds (17 mins 20 seconds) this is still for one monkey.

on the subject of monkeys, the time it will take can be expressed as "the time for one monkey to behave as required devided by the number of monkey"

so the probability for one monkey is 1/46^18

so the average for one monkey would be
425217348061789983250889965568 seconds (half of 46^18)
and for a million monkeys
425217348061789983250889.965568 seconds

4921497084048495176.514930157037 days
devide by 1461 (cause of varying number of days in any given year)
3368581166357628.4575735319350014 lots of four years

and
13474324665430.513830294127740005 millenia (thousand years)


answer = 13.5 million million milenia

Answer 2

I'll be thinking about this and will give you an answer soon.
we know that the sentence has 18 keys. so first we find the number of ways of choosing 18 keys in every order out of 46. let it be n. now the sentence is just one of the permutations. so the probability is 1/n. the probability for a million monkeys to get it each using a different key board is 10^6/n. this is done in 18sec. they may get it right or wrong. they have to do it atleast n/10^6 times so you multiply (n/10^6)*18 sec to get the time in sec. I've forgotten how to calculate getting n but i think i'll try to remember it. n = (45+44+43+...+1)*18!

Answer 3

This type of illustration about evolution has a fundamental flaw with it. Most mutations are either useless, a liability, or are fatal to the host, they aren't beneficial. This would be the same as saying if the monkey types the work "dead" before they typed the full phrase the typewriter is confiscated and the monkey shot. Most of the monkey's would be dead by the end of the first day.

Answer 4

Are the monkeys trained or not?

Answer 5

I PERSONNALY think that the monkey's would have to be THE MONKEES to EVER get it right!!

Answer 6

I think it would take longer for you to be able to spell "appreciate".