Statistics Chapter 5 (Probability I) Flashcards
What is probability
The proportion of times that a random phenomenon occurs in the long run over independent trails.
What are random phenomena
Everyday choices for which the outcome is uncertain
Deterministic phenomenon are occurances that are certain
Why is probability measured in the long run
Because the cumulative proportion is very variable in the short run but gets more accurate on average in the long run
What does it mean when a trial is independent and give an example of a common misconception
Different trials of a random phenomenon are independent if the outcome of any one trial is not affected by the outcome of any other trial.
A common misconception is that a probability for tails is higher if there were 4 times heads before.
When do you have to use subjective probability and what is the difference
When you don’t have objective probability collected through data, because you cannot practice the long run. You then assess the probability by taking account all of the information systems you have.
What’s the sample space
For a random phenomenon the sample space if the set of all possible outcomes.
All.possible values (heads and tails)
Explain what an event is
An event Is a subset of the sample space, an event corresponds to a paricular outcome or a group of possible outcomes.
Only heads
Odd numbers in a dice throw
How do you calculate the probability of an event P(A)
Number outcomes in event A
———————————————- = P(A)
Number of all outcomes
What are the three rules for finding probabilities
- Complement: P(A^c) = 1 - P(A)
- Addition rule: P(A or B) = P(A)+P(B) - P(A and B)
- Multiplication rule: P(A and B) = P(A) x P(B) ONLY IF INDEPENDENT
What does disjoint, intersection and union mean
Disjoint: two events that do not have any common outcomes
Intersection: P(A and B)
Union: P(A or B
Explain conditional probability
It gives the probability that when B occurs, A also occurs
P(A and B)
—————– = P(A|B)
P(B)
Example: diagnose is positive but also wrong
How do you find if two events events are independent
If P(A and B) = P(A) x P(B) Or If P(A|B) = P(A)
What is a probability model
A probability model looks at the possible outcomes for a sample space and provides assumptions on which the probabilities are based
NASA made a probability model to calculate how likely an engine failure is
How is probability on reality different from it in theory
In practice probability merely approximate reality. You cannot perform a perfect long-run and same sample probabilities (like in a dice) are very unlikely
