Card 1 of 20
EasyStudy card 1
Prompt
What is an outcome?
Answer
One possible result of a trial.
MathChapter 9: Categorical Data and Probability
Flashcards
Rules of Probability Flashcards
Twenty concise cards on outcomes, independence, replacement, AND paths, mutually exclusive OR events, and common denominator errors.
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Card 2 of 20
EasyStudy card 2
Prompt
What is a sample space?
Answer
The complete collection of possible outcomes under consideration.
Card 3 of 20
EasyStudy card 3
Prompt
For equally likely outcomes, how is \(P(A)\) calculated?
Answer
Divide the number of favorable outcomes by the total number of outcomes.
Formula
\[P(A)=\frac{\text{favorable}}{\text{total}}\]
Card 4 of 20
EasyStudy card 4
Prompt
What bounds must every probability satisfy?
Answer
\(0\le P(A)\le1\)
Formula
\[0\le P(A)\le1\]
Card 5 of 20
EasyStudy card 5
Prompt
What makes two events independent?
Answer
The result of one does not change the probability of the other.
Card 6 of 20
EasyStudy card 6
Prompt
What makes two events dependent?
Answer
The first result changes the remaining counts or probability of the second event.
Card 7 of 20
EasyStudy card 7
Prompt
Are standard draws with replacement independent or dependent?
Answer
Independent, because the original composition is restored.
Card 8 of 20
EasyStudy card 8
Prompt
Are standard draws without replacement independent or dependent?
Answer
Dependent, because the first draw changes what remains.
Card 9 of 20
MediumStudy card 9
Prompt
What is the independent AND rule?
Answer
\(P(A\text{ and }B)=P(A)P(B)\)
Formula
\[P(A\text{ and }B)=P(A)P(B)\]
Card 10 of 20
MediumStudy card 10
Prompt
How should the AND rule be adjusted for dependent events?
Answer
Multiply \(P(A)\) by the probability of \(B\) after \(A\) has occurred.
Formula
\[P(A\text{ and }B)=P(A)P(B\text{ following }A)\]
Card 11 of 20
EasyStudy card 11
Prompt
What happens to the second denominator without replacement?
Answer
It decreases by one because one item has been removed.
Card 12 of 20
MediumStudy card 12
Prompt
What happens to the second numerator after drawing from the same category without replacement?
Answer
It decreases by one along with the total.
Card 13 of 20
MediumStudy card 13
Prompt
When does the chapter-level OR addition rule apply?
Answer
When the events are mutually exclusive and cannot occur on the same trial.
Formula
\[P(A\text{ or }B)=P(A)+P(B)\]
Card 14 of 20
EasyStudy card 14
Prompt
What is a mutually exclusive pair of events?
Answer
Two events that cannot both occur in the same trial.
Example
A single number-cube roll is 1 or 6.
Card 15 of 20
HardStudy card 15
Prompt
How should an overlapping OR event be handled in a small finite sample space?
Answer
List or count each distinct favorable outcome once so overlap is not double-counted.
Card 16 of 20
EasyStudy card 16
Prompt
What operation usually corresponds to AND?
Answer
Multiplication along the complete event path.
Card 17 of 20
MediumStudy card 17
Prompt
How do you find the probability of drawing two items from the same category?
Answer
Calculate each matching branch separately, then add the mutually exclusive branch probabilities.
Card 18 of 20
EasyStudy card 18
Prompt
A draw is replaced. Should the second denominator decrease?
Answer
No. Replacement restores the original total before the next draw.
Card 19 of 20
MediumStudy card 19
Prompt
Why can a favorable-outcome count alone not be a probability?
Answer
It must be divided by the size of the equally likely sample space.
Card 20 of 20
HardStudy card 20
Prompt
What is the safest method for a three-stage probability question?
Answer
Track the available category counts and total at every stage, then multiply the path probabilities.
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