Question

1. (Review) Let's examine the concept of "never happens" from a math/physics point of view. Suppose that 1010 monkeys (about three times the current human population on earth) have been seated at a computer with a word-processor program throughout of the age of universe, 1018 sec. (Forget about where to get these monkeys and computer, how to keep them alive that long, etc.) Suppose one monkey can hit 10 keys on the keyboard per second, and cach keyboard has 44 keys (26 lower case letters 10 numbers 8 punctuation keys). Let's explore a probability that a known book, say Hamlet by Shakespcare, is produced by thesc monkeys. Hamlet contains roughly 105 characters (a) Can you estimate the probability that any given sequence of 10 characters typed at random wil come out in a correct sequence, i.e. the sequence of Hamlet? (This sequence does not have to be produced by only one monkey). Give your answer in the form of x What is the value of X? (b) What is probability that these moneys produce Hamlet in the age of the universe? Will it happen? Or will it never happen?

Answer 1