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Questions and Answers
What does the probability of an event must lie between?
What does the probability of an event must lie between?
Define an experiment in probability.
Define an experiment in probability.
An experiment refers to any situational activity that involves chance.
In a typical experiment, what is the sample space?
In a typical experiment, what is the sample space?
The experimental probability of an event E is the ratio of the number of times event E occurs to the total number of _____
The experimental probability of an event E is the ratio of the number of times event E occurs to the total number of _____
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What is the probability of rolling a 2 on a fair six-sided die?
What is the probability of rolling a 2 on a fair six-sided die?
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If a box contains 4 red marbles, 5 yellow marbles, and 3 green marbles, what is the probability of picking a yellow marble?
If a box contains 4 red marbles, 5 yellow marbles, and 3 green marbles, what is the probability of picking a yellow marble?
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Experimental probability only applies to theoretical outcomes.
Experimental probability only applies to theoretical outcomes.
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What are mutually exclusive events?
What are mutually exclusive events?
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Match the following terms with their definitions:
Match the following terms with their definitions:
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What can be defined as a collection of outcomes of an experiment?
What can be defined as a collection of outcomes of an experiment?
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What are the two main types of probability?
What are the two main types of probability?
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What are the two types of probability?
What are the two types of probability?
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What is the sample space for rolling a die?
What is the sample space for rolling a die?
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The probability of an event must lie between 0 and 1, inclusive.
The probability of an event must lie between 0 and 1, inclusive.
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What does an experiment refer to in probability?
What does an experiment refer to in probability?
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Which theorem states that the remainder of the division of a polynomial can be found by evaluating the polynomial at a specific point?
Which theorem states that the remainder of the division of a polynomial can be found by evaluating the polynomial at a specific point?
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The intersection of sets A and B is the set whose elements are common to set A and ______.
The intersection of sets A and B is the set whose elements are common to set A and ______.
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How would you define simple events?
How would you define simple events?
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What is the probability of rolling a 2 on a fair die?
What is the probability of rolling a 2 on a fair die?
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What are compound events?
What are compound events?
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Which of these is NOT a type of compound event?
Which of these is NOT a type of compound event?
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What is meant by the term 'sample space'?
What is meant by the term 'sample space'?
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Study Notes
Probability
- Probability is the likelihood of an event occurring. The probability of an event must lie between 0 and 1, inclusive (0 ≤ 𝑃(𝐸) ≤ 1).
- The closer the probability of an event is to 1, the more likely the event is to happen.
Experiment and Events
- An experiment is any activity involving chance, such as observing or taking measurements. Examples include tossing a coin or rolling a die.
- Outcomes are the possible results of an experiment.
- Sample space is the list of all possible outcomes.
- Events are any subset of the sample space, or any collection of outcomes of an experiment.
Types of Probability
- Experimental probability is found by dividing the number of times an event occurs by the total number of trials: - (Number of times event E occurs) / (Total number of trials)
- Theoretical probability is found by dividing the number of ways an event can occur by the total number of possible outcomes: - (Number of ways the event can occur) / (Number of possible outcomes)
Compound Events
- Simple events involve a single outcome.
- Compound events involve multiple possible outcomes.
- Mutually exclusive events cannot occur simultaneously.
- Non-mutually exclusive events can occur simultaneously.
- Independent events do not affect the outcome of other events.
- Dependent events do affect the outcome of other events.
Union and Intersection of Sets
- The union of sets (A U B) includes all elements in set A or set B.
- The intersection of sets (A ∩ B) includes all elements that are in both set A and set B.
Probability
- Probability is the likelihood of an event happening.
- The probability of an event must be between 0 and 1.
- The closer the probability is to 1, the more likely the event is to happen.
Terms
- An experiment is a situational activity with chance, involving observations or measurements.
- Outcomes are possible results of an experiment.
- The sample space is the list of all possible outcomes of an experiment.
- An event is a subset of the sample space, a collection of possible outcomes.
Types of Probability
- Experimental Probability is used when an experiment is performed multiple times.
- Theoretical Probability assumes all outcomes are equally likely.
Experimental Probability
- The probability of an event is calculated by dividing the number of times the event occurs by the total number of trials.
Theoretical Probability
- The probability of an event is calculated by dividing the number of ways the event can occur by the number of possible outcomes.
Types of Compound Events
- Mutually Exclusive Events: Events that cannot occur at the same time.
- Non-Mutually Exclusive Events: Events that can occur at the same time.
- Independent Events: Events where the outcome of one does not affect the outcome of the other.
- Dependent Events: Events where the outcome of one event affects the outcome of the other.
Union and Intersection of Sets
- The union of sets A and B (A U B) is the set containing elements that belong to either set A or B or both sets.
- The intersection of sets A and B (A ∩ B) is the set containing elements found in both set A and set B.
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Description
Test your understanding of basic probability concepts, including experiments, events, and the types of probability. This quiz covers key definitions and formulas that help in calculating experimental and theoretical probabilities. Strengthen your math skills with practical examples and explanations.
