3.1 Terminology

Experiment: is a planned operation carried out under the controlled condition
Outcome: Result of an experiment
Sample space: a set of all possible outcomes
Event: any combination of outcomes that are usually represented by the letters A and B.
Equally Likely: Each outcome of an experiment has the same probability.
Probability: the chance of the outcome of an event
“OR” Event: an outcome is in the event A OR B if the outcome is in A or is in B or is in both A and B.
"AND" Event: an outcome is in the event A AND B if the outcome is in both A and B at the same time.
Conditional probability: A given B is written P(A|B). P(A|B) is the probability that event A will occur given that event B has already occurred
Complement: A given B is written P(A|B’)

Formula for P(A|B)

3.2 Independent and Mutually Exclusive Events

Independent: One event occurring does not affect the chance that the other event occurs.
Sampling with replacement: then events are considered to be independent, meaning the result of the first pick will not change the probabilities for the second pick.
Sampling without replacement: the probabilities for the second pick are affected by the result of the first pick. The events are considered to be dependent or not independent.
The events are independent if this is true:
- P(A|B) = P(A)
- P(B|A) = P(B)
- P(A AND B) = P(A)P(B)
Mutually exclusive: If events occur at the same time
- P(A and B) = 0

Multiplication Rule: If A and B are two events defined on a sample space, then: P(A AND B) = P(B)P(A|B). A and B are independent, then P(A|B) = P(A). Then P(A AND B) = P(A|B)P(B) becomes P(A AND B) = P(A)P(B)
- P(A|B) = 𝑃(𝐴 AND 𝐵) / 𝑃(𝐵)
Addition Rule: If A and B are defined on a sample space, then: P(A OR B) = P(A) + P(B) - P(A AND B). If A and B are mutually exclusive, then P(A AND B) = 0. Then P(A OR B) = P(A) + P(B) - P(A AND B) becomes P(A OR B) = P(A) + P(B)

Contingency table: provides a way of portraying data that can facilitate calculating probabilities.

Tree diagrams: used to determine the outcomes of an experiment. It consists of "branches" that are labeled with either frequencies or probabilities.
Venn diagrams: a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events.

Home $knowt breadcrumb$

Experiment: is a planned operation carried out under the controlled condition
Outcome: Result of an experiment
Sample space: a set of all possible outcomes
Event: any combination of outcomes that are usually represented by the letters A and B.
Equally Likely: Each outcome of an experiment has the same probability.
Probability: the chance of the outcome of an event
“OR” Event: an outcome is in the event A OR B if the outcome is in A or is in B or is in both A and B.
"AND" Event: an outcome is in the event A AND B if the outcome is in both A and B at the same time.
Conditional probability: A given B is written P(A|B). P(A|B) is the probability that event A will occur given that event B has already occurred
Complement: A given B is written P(A|B’)

Formula for P(A|B)

Independent: One event occurring does not affect the chance that the other event occurs.
Sampling with replacement: then events are considered to be independent, meaning the result of the first pick will not change the probabilities for the second pick.
Sampling without replacement: the probabilities for the second pick are affected by the result of the first pick. The events are considered to be dependent or not independent.
The events are independent if this is true:
- P(A|B) = P(A)
- P(B|A) = P(B)
- P(A AND B) = P(A)P(B)
Mutually exclusive: If events occur at the same time
- P(A and B) = 0

Multiplication Rule: If A and B are two events defined on a sample space, then: P(A AND B) = P(B)P(A|B). A and B are independent, then P(A|B) = P(A). Then P(A AND B) = P(A|B)P(B) becomes P(A AND B) = P(A)P(B)
- P(A|B) = 𝑃(𝐴 AND 𝐵) / 𝑃(𝐵)
Addition Rule: If A and B are defined on a sample space, then: P(A OR B) = P(A) + P(B) - P(A AND B). If A and B are mutually exclusive, then P(A AND B) = 0. Then P(A OR B) = P(A) + P(B) - P(A AND B) becomes P(A OR B) = P(A) + P(B)

Contingency table: provides a way of portraying data that can facilitate calculating probabilities.

Tree diagrams: used to determine the outcomes of an experiment. It consists of "branches" that are labeled with either frequencies or probabilities.
Venn diagrams: a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events.