What is the definition of conditional probability?
Conditional probability is the probability of an event occurring given that another event has already occurred.
Fill in the blank: The formula for conditional probability is P(A | B) = _____ / P(B).
P(A and B)
What does the notation P(A | B) signify?
It signifies the probability of event A occurring given that event B has occurred.
If P(B) = 0.5 and P(A and B) = 0.2, what is P(A | B)?
0.4
Short answer: How can conditional probability be useful in real-world scenarios?
It helps in making decisions based on the occurrence of related events, such as in medical testing, risk assessment, and predictive modeling.
What does the law of large numbers state?
As the number of trials of a statistical experiment or observation increases, the relative frequency of a designated event becomes closer to the theoretical probability of that event.
What are mutually exclusive events?
Events that cannot occur together.
What are independent events?
Events where the occurrence of one does not change the probability of the occurrence of the other.
What does the complement rule provide?
The probability that an event will not occur.
What does P(A or B) mean?
What is a formula for it?
The probability that at least one of two specified events will occur.
P(A or B) = P(A) + P(B)- P(A and B)
What does the multiplication rule provide?
The probability that two events will occur together.
To determine the probability of equally likely events, what do we need to know?
How many outcomes are possible.
What devices help determine the total number of outcomes of a statistical experiment?
- Tree diagrams
- Counting rules (multiplication rule of counting, permutations rule, combinations rule)
What does P(A and B) represent in probability theory?
P(A and B) represents the probability that both events A and B occur simultaneously.
Fill in the blank: If A and B are not independent, P(A and B) is calculated using this formula:
P(A and B) = P(A) * P(B | A)
What is the formula for P(A and B) if A and B are mutually exclusive?
P(A and B) = 0
