Question

Suppose that a monkey is seated at a computer keyboard and randomly strikes the 26 letter keys and the space bar. Find the probability that its first 39 characters (including spaces) will be "to be or not to be that is the question". (Leave your answer as a formula.)

Name: Problem 25, Chapter 7: Finite Mathematics and Applied Calculus
Uploaded: 2021-10-17T16:18:01-08:00
Duration: 1 min 30 s
Channel: Nick Johnson
Description: Suppose that a monkey is seated at a computer keyboard and randomly strikes the 26 letter keys and the space bar. Find the probability that its first 39 characters (including spaces) will be "to be or not to be that is the question". (Leave your answer as a formula.)

   Suppose that a monkey is seated at a computer keyboard and randomly strikes the 26 letter keys and the space bar. Find the probability that its first 39 characters (including spaces) will be "to be or not to be that is the question". (Leave your answer as a formula.)

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 5th Edition

Chapter 7, Problem 25

Instant Answer

Solved by Expert Nick Johnson

10/17/2021

Step 1

The monkey has 27 choices (26 letters and a space bar) for each of the 39 characters it types. Therefore, the total number of possible outcomes is $27^{39}$. Show more…

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Suppose that a monkey is seated at a computer keyboard and randomly strikes the 26 letter keys and the space bar. Find the probability that its first 39 characters (including spaces) will be "to be or not to be that is the question". (Leave your answer as a formula.)

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Key Concepts

Independent Events

This concept refers to events where the outcome of one occurrence has no influence on the outcomes of subsequent occurrences. In the problem, each key strike by the monkey is independent, meaning the probability for each keystroke is unaffected by previous keystrokes.

Sample Space and Outcome Counting

The sample space is the set of all possible outcomes for a given event. Here, the sample space for a single keystroke includes the 26 letters and the space bar, totaling 27 outcomes. Correctly identifying the size of the sample space for each event is key to setting up the probability calculation.

Multiplication Rule of Probability

This rule states that if multiple events are independent, the probability of all events occurring in a specific sequence is the product of their individual probabilities. In this case, the probability that each of the 39 keystrokes is exactly as desired is found by multiplying the probability for each keystroke.

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