Notation When randomly selecting a new smartphone, D denotes the ...

4. Probability

Complements

Statistics

4. Probability

Complements

2:18 minutes

Problem 4.2.1

Textbook Question

Notation When randomly selecting a new smartphone, D denotes the event that it has a manufacturing defect. What do P(D) and P(D) represent?

Verified step by step guidance

Step 1: Understand the notation. In probability, 'P(D)' represents the probability of event 'D' occurring. Here, 'D' is the event that a randomly selected smartphone has a manufacturing defect.

Step 2: Clarify the meaning of 'P(D)'. It quantifies the likelihood of the event 'D' happening, expressed as a value between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

Step 3: Recognize that 'P(D)' is a mathematical representation of the probability. For example, if 5% of smartphones have defects, then P(D) = 0.05.

Step 4: If the problem also refers to 'P(D)', it is likely asking for the same probability value, as 'P(D)' is the standard notation for the probability of event 'D'.

Step 5: To calculate P(D) in practice, you would divide the number of defective smartphones by the total number of smartphones in the sample or population, using the formula: <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>P</mi><mo>(</mo><mi>D</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>Number</mi><mo> </mo><mi>of</mi><mo> </mo><mi>defective</mi><mo> </mo><mi>smartphones</mi></mrow><mrow><mi>Total</mi><mo> </mo><mi>number</mi><mo> </mo><mi>of</mi><mo> </mo><mi>smartphones</mi></mrow></mfrac></mrow></math>.

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 number between 0 and 1. In this context, P(D) represents the probability that a randomly selected smartphone has a manufacturing defect. Understanding probability is essential for interpreting the likelihood of events in statistics.

Event

An event in probability is a specific outcome or a set of outcomes from a random experiment. In this case, D is the event that a smartphone has a manufacturing defect. Recognizing events helps in calculating probabilities and understanding the context of statistical analysis.

Notation in Probability

Notation in probability provides a standardized way to represent events and their probabilities. P(D) specifically denotes the probability of event D occurring. Familiarity with this notation is crucial for effectively communicating and solving problems in statistics.

Watch next

Master Complementary Events with a bite sized video explanation from Patrick

Start learning

����app