Question 8.74

43. You may have heard that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time could eventually type a particular chosen text, such as the complete works of Shakespeare. Let’s focus on a monkey who just types the letters , and in random order in three-letter sequences.

  1. How many possible three-letter “words” can the monkey type using only these letters?
  2. Which of these are words in an English dictionary?
  3. What is the probability that the word the monkey typed is in an English dictionary?

43.

(a) The possibilities are aps, asp, pas, psa, sap, spa.

(b) Asp, pas, sap, and spa are English words.

(c) The probability is . The answer can also be expressed as exactly or approximately 66.7%.