Podcast
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?
- 0.5
- 1.5 (correct)
- 0
- 1
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.
Which of the following is the most accurate description of probability?
Which of the following is the most accurate description of probability?
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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