Monkey unable to type all of Hamlet before the universe ends but could type "bananas" before it dies

The "infinite monkey theorem" suggests that if you gave a monkey an infinite amount of time to randomly hit keys on a typewriter, it would eventually produce the complete works of Shakespeare—Hamlet included—purely by chance. Unfortunately, it won't happen before the end of the universe. That's according to a new scientific study by mathematicians at the University of Technology Sydney.

"The Infinite Monkey Theorem only considers the infinite limit, with either an infinite number of monkeys or an infinite time period of monkey labour," says researcher Stephen Woodcock. "We decided to look at the probability of a given string of letters being typed by a finite number of monkeys within a finite time period consistent with estimates for the lifespan of our universe."

From UTS:

For number-crunching purposes, the researchers assumed that a keyboard contains 30 keys including all the letters of the English language plus common punctuation marks.

As well as a single monkey, they also did the calculations using the current global population of around 200,000 chimpanzees, and they assumed a rather productive typing speed of one key every second until the end of the universe in about 10^100 years – that's a 1 followed by 100 zeros[…]

…Even with all chimps enlisted, the Bard's entire works (with around 884,647 words) will almost certainly never be typed before the universe ends.

"It is not plausible that, even with improved typing speeds or an increase in chimpanzee populations, monkey labour will ever be a viable tool for developing non-trivial written works," the authors muse.

Incredibly, there's about a 5% chance that a single chimp could type the word "bananas" at least once within its lifetime.

Previously:
• How math people look at math, and why it works
• Why did this famous mathematician want a 17-sided shape on his tombstone?
• Mathematicians analyze the geometries of the Pringle