10 Questions
What is the set of all possible outcomes called in a random experiment?
Sample space
In the random experiment of throwing a fair die, what is the sample space?
{1, 2, 3, 4, 5, 6}
What are events in the context of random experiments?
Sample space subsets
What does the sample space {RR, RC, RS, CR, CC, CS, SR, SC, SS} represent?
Possible weather outcomes
What is the event A when playing the board game and needing to roll 4 or above to win?
{4, 5, 6}
Which set is denoted as an empty event?
{}
What does a partition of subsets D1,..., Ds of Ω entail?
Mutually disjoint events forming the sample space
When does the classical definition of probability apply?
For experiments with equally likely outcomes
What does P(Ω) represent under the classical definition?
The probability of event Ω
Under the classical definition, what is P(A ∪ B) if events A and B are disjoint?
P(A) + P(B)
Study Notes
Random Experiments and Events
- In a random experiment, the set of all possible outcomes is called the sample space.
Throwing a Fair Die
- The sample space of throwing a fair die is {1, 2, 3, 4, 5, 6}.
Events
- In the context of random experiments, events are subsets of the sample space.
Sample Space Example
- The sample space {RR, RC, RS, CR, CC, CS, SR, SC, SS} represents the outcomes of tossing two coins, where R is heads and S is tails.
Event Example
- When playing a board game, the event A is rolling 4 or above to win.
Empty Event
- The empty set, denoted by ∅, represents an empty event.
Partition of Subsets
- A partition of subsets D1,..., Ds of Ω entails that every outcome in Ω belongs to exactly one of the subsets Di.
Classical Definition of Probability
- The classical definition of probability applies when all outcomes in the sample space are equally likely.
Probability of Sample Space
- Under the classical definition, P(Ω) represents 1, or certainty.
Probability of Disjoint Events
- Under the classical definition, if events A and B are disjoint, P(A ∪ B) is the sum of P(A) and P(B).
Test your understanding of random experiments, sample space, and possible outcomes. Explore the concept of experimental outcomes and their relationship to chance in statistics.
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