Monkeys typing Shakespeare Since events of low probability e

Monkeys typing Shakespeare: Since events of low probability eventually happen if you observe enough trials, a monkey randomly pecking on a typewriter could eventually write a Shakespeare play just by chance. Let\'s see how hard it would be to type the title of Macbeth properly. Assume 50 keys for letters and numbers and punctuation. Find the probability that the first seven letters that a monkey types are Macbeth. (Even if the monkey can type 60 strokes a minute and never sleeps, if we consider each sequence of seven keystrokes as a trial, we would wait on the average over 100,000 years before seeing this happen!)

Solution

since the typewriter has 50 keys

the chance of hitting any key is 1/50

so , probability of a letter typed by monkey being a letter of macbeth is 1/50

probability that the first sevenleeters monkey type are macbeth

= 1/50 * 1/50 * 1/50 * 1/50 *1/50 *1/50 * 1/50

= 1/50^7

= 1.28*10^-12