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Questions and Answers
In probability theory, which of the following values can a probability NOT take?
In probability theory, which of the following values can a probability NOT take?
Probability is solely determined by the number of successful outcomes; the total number of possible outcomes does not influence the calculation.
Probability is solely determined by the number of successful outcomes; the total number of possible outcomes does not influence the calculation.
False (B)
What is the probability of an impossible event?
What is the probability of an impossible event?
0
The probability of an event occurring ranges from ______ to 1.
The probability of an event occurring ranges from ______ to 1.
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Which of the following is the most accurate description of probability?
Which of the following is the most accurate description of probability?
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Flashcards
Probability
Probability
A measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
Event
Event
An outcome or a set of outcomes from a probability experiment.
Sample Space
Sample Space
The set of all possible outcomes of a probability experiment.
Independent Events
Independent Events
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Complementary Events
Complementary Events
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Study Notes
Engineering Data Analysis - Probability
- Probability is the likelihood of an event occurring. It's measured on a scale from 0 to 1 (or 0% to 100%).
- A probability of 1 indicates the event will definitely occur.
- A probability of 0 indicates the event is impossible.
- Sample spaces list all possible outcomes.
- Events are subsets of the sample space.
- Mutually exclusive events cannot occur at the same time.
- Rules of addition and multiplication help determine the probabilities of events.
Probability of an Event
- Probability (P(E)) = (number of elements in the event set) / (number of elements in the sample space) = n(E) / n(S)
- All probabilities in a sample space must add up to 1.
Key Rules
- Addition Rule (Mutually Exclusive): P(A ∪ B) = P(A) + P(B)
- Addition Rule (Not Mutually Exclusive): P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
- Multiplication Rule (Independent): P(A ∩ B) = P(A) × P(B)
- Multiplication Rule (Dependent): P(A ∩ B) = P(A) × P(B|A)
Other Important Concepts
- Conditional Probability (P(B|A)): The probability of event B occurring, given that event A has already occurred.
- Complement of an event (A'): Represents the event where A does not occur. P(A') = 1 - P(A)
- Intersection (A ∩ B): The set of outcomes that are common to both events A and B.
- Union (A ∪ B): The set of outcomes present in either event A or event B or both.
- Sample Space (S): The set of all possible outcomes of an event.
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Description
This quiz covers essential concepts of probability, including sample spaces, events, and the rules of addition and multiplication. Learn how to calculate probabilities and understand how they apply in engineering contexts. Test your knowledge on mutually exclusive events and their probabilities.
