What is the probability of an outcome?
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The likelihood that the outcome will occur when the uncertainty is resolved.
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What is the probability of an outcome?
The likelihood that the outcome will occur when the uncertainty is resolved.
How is an event defined in probability?
An event is a collection of outcomes.
What are subjective probabilities?
Probabilities that cannot be estimated from long-run proportions and are normally opinions or guesses given by people.
What is the Rule of Complements?
The probability of an event occurring is 1 minus the probability of the event not occurring.
Can you provide an example of a subjective probability?
The probability that Brazil will win the next world cup.
What is the probability of getting at most two heads when three unbiased coins are tossed?
To find the probability of getting at most two heads, we can use the rule of complements by finding the probability of getting three heads and subtracting it from 1.
What is the relative frequency of an event?
The proportion of times that the event occurs out of the number of times the random experiment is run.
What type of probabilities are based on opinions or guesses given by people?
Subjective probabilities.
What is a Venn diagram used for in probability?
To visually represent the relationships between different events and their intersections.
How can a relative frequency be recorded?
As a proportion or a percentage.
What does a Venn diagram for Non-Mutually Exclusive Events show?
The overlap between two events, indicating that they can occur together.
What are objective probabilities?
Probabilities that can be estimated from long-run proportions (normally via data collection).
What is the probability of picking a spade from a deck of cards?
P(E) = 13/52
What does the joint event A ∩ B represent?
The intersection of events A and B, showing the outcomes that are common to both events.
What is an experiment in probability?
An activity that results in one of several possible outcomes.
What is the probability of picking a seven from a deck of cards?
P(F) = 4/52
What is the range of probability for any event?
A number between zero and one.
What does it mean for outcomes to be mutually exclusive?
No two outcomes can occur together.
What is the total number of tickets?
What are equally likely events?
Events where outcomes have an equal chance of occurring.
What does a larger probability correspond to?
Greater likelihood.
What does it mean for outcomes to be collectively exhaustive?
At least one of the outcomes must occur when the experiment is performed.
How many tickets have numbers that are multiples of 2?
Give an example of equally likely events.
Tossing a balanced coin or throwing a fair die.
What does a probability of 1.0 indicate about an event?
It is virtually certain to occur.
What is the set of all possible outcomes of an experiment called?
The sample space of the experiment.
What are mutually exclusive events?
Events that cannot occur at the same time.
What does the symbol 'E' represent in the context of card picking?
The event of picking a spade.
How many tickets have numbers that are multiples of 3?
What are the assumptions for equally likely events?
Assuming balanced coin when it is tossed, assuming fair die when it is thrown, and assuming tickets are all in exactly the same appearance when they are drawn.
What is the Second Law of Probability for mutually exclusive events?
If A and B are mutually exclusive events, then the probability of either A or B occurring is the sum of the probabilities of A and B.
What does the symbol 'F' represent in the context of card picking?
The event of picking a seven.
What is the probability of drawing a ticket with a number that is a multiple of 2 or 3?
5/6 or 0.8333.
What happens if the assumption of equally likely events is not correct?
The probabilities derived theoretically may not be accurate.
What does a Venn diagram for mutually exclusive events look like?
Two separate circles that do not overlap.
What does a probability of 0.0 indicate about an event?
It is certain not to occur.
