AdvancedTopic 77 of 104Engineering Mathematics
Probability basics
Quantifies uncertainty; probabilities lie between 0 and 1 and total 1 over all outcomes.
In depth
Probability P(A) of an event lies in [0,1]; P(A or B)=P(A)+P(B)-P(A and B). Independent events satisfy P(A and B)=P(A)P(B). Counting uses permutations n!/(n-r)! and combinations n!/(r!(n-r)!).
Key points
- Sample space lists outcomes
- Complement rule: 1-P(A)
- Frequentist vs Bayesian interpretation
ExampleThe chance of two components both working with 0.9 each, independently, is 0.81.
Probability quantifies uncertainty in loads, failures and measurements, so it is necessary for reliable design and risk decisions.
What is Probability basics?
Quantifies uncertainty; probabilities lie between 0 and 1 and total 1 over all outcomes.
Why is it important to understand probability basics?
Probability quantifies uncertainty in loads, failures and measurements, so it is necessary for reliable design and risk decisions.
What do the axioms of probability require?
Probabilities are non-negative, the probability of the whole sample space is one, and the probability of disjoint events adds.
What is the difference between independent and mutually exclusive events?
Independent events do not affect each other's probability. Mutually exclusive events cannot happen together, and that makes them strongly dependent.
How is Probability basics used in practice?
Typical applications include estimating the chance a sensor reads out of range during a test, assessing the probability that two parallel systems both fail and estimating the chance a batch contains a defective part.
What should I learn before Probability basics?
Study "Boundary and initial conditions" first (topic 76 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
What are the key points of Probability basics?
Sample space lists outcomes. Complement rule: 1-P(A). Frequentist vs Bayesian interpretation.
Can you give an example of Probability basics?
The chance of two components both working with 0.9 each, independently, is 0.81.
What comes after Probability basics?
The next topic is "Conditional probability and Bayes", which builds directly on this one.
How difficult is Probability basics?
It is classed as Advanced in Engineering Mathematics (topic 77 of 104). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Engineering Mathematics.