Question

In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.

Square Peg Sydney Smith wrote in “On the Conduct of the Understanding” that it is impossible to fit a square peg in a round hole.

Short answer

The probability of fitting a square peg in a round hole is 0.

Step-by-step solution

Given information

In the book “On the Conduct of the Understanding,” the author wrote that a square peg was impossible to fit in a round hole.

Define probability

To quantify the likelihood of the occurrence of any event, you can define itsprobability.

Mathematically, it is written as

$P\left(E\right)=\frac{\text{Number}\text{of}\text{outcomes}\text{in}\text{favour}\text{of}E}{\text{Total}\text{number}\text{of}\text{outcomes}}$

Its value lies between 0 and 1.

The interpretation of two extreme values is:

• A probability value of 0 indicates an impossible event
• A probability value of 1 indicates a sure event.

Calculate the probability 

Let E be the event of fitting a square peg into a round hole.

Since it is “impossible” for E to happen, its probability is zero.

Therefore, the probability of fitting a square peg in a round hole is zero.