In Exercises 13–20, express the indicated degree of likelihood as...

4. Probability

Basic Concepts of Probability

Statistics

4. Probability

Basic Concepts of Probability

1:16 minutes

Problem 4.1.19

Textbook 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.

Verified step by step guidance

Understand the problem: The task is to express the degree of likelihood of an event (in this case, the impossibility of fitting a square peg into a round hole) as a probability value between 0 and 1. Probability values range from 0 (impossible event) to 1 (certain event).

Recall the definition of probability: Probability is a measure of how likely an event is to occur. An event that is described as 'impossible' has a probability of 0.

Interpret the statement: The phrase 'it is impossible to fit a square peg in a round hole' indicates that the event cannot occur under any circumstances.

Assign the probability value: Based on the interpretation of 'impossible,' assign a probability value of 0 to this event.

Conclude: The probability of fitting a square peg into a round hole, as described in the problem, is 0. This is the final probability value expressed between 0 and 1.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a value between 0 and 1. A probability of 0 indicates that the event cannot happen, while a probability of 1 indicates certainty that the event will occur. Understanding how to calculate and interpret probabilities is essential for analyzing situations involving uncertainty.

Event

In probability theory, an event is a specific outcome or a set of outcomes from a random experiment. For example, in the context of fitting a square peg into a round hole, the event could be defined as 'the peg fits.' Identifying the event of interest is crucial for determining its probability.

Sample Space

The sample space is the set of all possible outcomes of a random experiment. In the case of fitting a square peg into a round hole, the sample space would include all configurations of the peg and hole. Understanding the sample space helps in calculating the probability of specific events by providing a complete context for the possible outcomes.

Watch next

Master Introduction to Probability with a bite sized video explanation from Patrick

Start learning

����app

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.