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.
p.12
Objective Probabilities
What are objective probabilities?
Probabilities that can be estimated from long-run proportions (normally via data collection).
p.9
Mutually Exclusive Events
What does the joint event A ∩ B represent?
The intersection of events A and B, showing the outcomes that are common to both events.
p.4
First Law of Probability
What is the range of probability for any event?
A number between zero and one.
p.11
Equally Likely Events
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.
p.11
Equally Likely Events
What happens if the assumption of equally likely events is not correct?
The probabilities derived theoretically may not be accurate.
p.4
First Law of Probability
What does a probability of 0.0 indicate about an event?
It is certain not to occur.
p.3
Event as a Collection of Outcomes
How is an event defined in probability?
An event is a collection of outcomes.
p.9
Event as a Collection of Outcomes
What is a Venn diagram used for in probability?
To visually represent the relationships between different events and their intersections.
p.2
Event as a Collection of Outcomes
What does it mean for outcomes to be collectively exhaustive?
At least one of the outcomes must occur when the experiment is performed.
p.2
Space and Experiment Outcomes
What is the set of all possible outcomes of an experiment called?
The sample space of the experiment.
p.2
Mutually Exclusive Events
What does it mean for outcomes to be mutually exclusive?
No two outcomes can occur together.
p.13
Subjective Probabilities
What are subjective probabilities?
Probabilities that cannot be estimated from long-run proportions and are normally opinions or guesses given by people.
p.12
Objective Probabilities
How can a relative frequency be recorded?
As a proportion or a percentage.
What is the Rule of Complements?
The probability of an event occurring is 1 minus the probability of the event not occurring.
p.8
Mutually Exclusive Events
What are mutually exclusive events?
Events that cannot occur at the same time.
p.8
Second Law of Probability
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.
p.3
Probability of an Outcome
What is the probability of an outcome?
The likelihood that the outcome will occur when the uncertainty is resolved.
p.13
Subjective Probabilities
Can you provide an example of a subjective probability?
The probability that Brazil will win the next world cup.
p.12
Objective Probabilities
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.
p.13
Subjective Probabilities
What type of probabilities are based on opinions or guesses given by people?
Subjective probabilities.
p.9
Mutually Exclusive Events
What does a Venn diagram for Non-Mutually Exclusive Events show?
The overlap between two events, indicating that they can occur together.
p.2
Space and Experiment Outcomes
What is an experiment in probability?
An activity that results in one of several possible outcomes.
p.11
Equally Likely Events
What are equally likely events?
Events where outcomes have an equal chance of occurring.
p.11
Equally Likely Events
Give an example of equally likely events.
Tossing a balanced coin or throwing a fair die.
p.4
First Law of Probability
What does a probability of 1.0 indicate about an event?
It is virtually certain to occur.
p.5
Event as a Collection of Outcomes
What does the symbol 'E' represent in the context of card picking?
The event of picking a spade.
p.5
Event as a Collection of Outcomes
What does the symbol 'F' represent in the context of card picking?
The event of picking a seven.
p.8
Space and Experiment Outcomes
What does a Venn diagram for mutually exclusive events look like?
Two separate circles that do not overlap.
