2 Basic Concepts of Probability

Chapter Overview and Learning Objectives

  • To understand the fundamental concepts of probability.
  • To understand the differences between various probability rules.
  • To apply the probability rules to reliability examples.
  • To learn the required assumptions of the probability rules.

2.1 Probability

Probability is a ratio of specific outcomes to total possible outcomes. In our daily lives, we hear from the news about the chance of rainfall, which could be an example of probability. The equation for probability is shown here.

upper P left-parenthesis normal upper A right-parenthesis equals StartFraction n Over upper N EndFraction (2.1)

The n indicates the number of elements in events. The N denotes the number of elements in the sample space. Thus, P(A) means the probability of obtaining an outcome A. Probability is always ranged between 0 and 1 (Equation 2.2). If P(A) = 0, the event cannot occur. If P(A) = 1, a sure event is expected.

0 less-than-or-equal-to upper P left-parenthesis normal upper A right-parenthesis less-than-or-equal-to 1 (2.2)

Example 2.1 If you flip a coin, what are the possible outcomes? If you are interested in seeing a tail, what is the probability?

Answer:

Possible outcomes = {Head, Tail}.

upper P left-parenthesis normal upper T normal a normal i normal l right-parenthesis equals one-half

2.1.1 The Importance of Probability in Reliability

The probability concept can be effectively applied to the field of reliability. Quantitative ...

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