Questions and Answers
What is the formula for the probability of an event and its complement?
What is the condition for two events to be mutually exclusive?
What is the formula for the probability of the union of two mutually exclusive events?
What is the formula for the addition rule for any two events A and B?
Signup and view all the answers
What does the symbol $A'$ represent in probability?
Signup and view all the answers
What is the formula for the probability of two independent events?
Signup and view all the answers
What is the condition for the addition rule to simplify to $P(A ext{ or } B) = P(A) + P(B)$?
Signup and view all the answers
What is the sample space represented by in probability?
Signup and view all the answers
What is the formula for the complementary rule?
Signup and view all the answers
What is the condition for two events to be dependent?
Signup and view all the answers
What is the condition for two events A and B to be independent?
Signup and view all the answers
What is the relationship between mutual exclusivity and independence?
Signup and view all the answers
What is the term for events that are mutually exclusive and make up the whole sample space?
Signup and view all the answers
What is the purpose of the product rule?
Signup and view all the answers
What is the difference between the addition rule and the product rule?
Signup and view all the answers
Why is it important to verify if $P(A ext{ and } B) = P(A) imes P(B)$ when testing for independence?
Signup and view all the answers
What is the relationship between the probabilities of two events and their union and intersection as expressed by the addition rule?
Signup and view all the answers
What is the condition for the addition rule to simplify to P(A or B) = P(A) + P(B)?
Signup and view all the answers
What is represented by P(not A)?
Signup and view all the answers
When are two events A and B independent?
Signup and view all the answers
What can be concluded about two events A and B if P(A and B) = 0?
Signup and view all the answers
What is necessary to verify when testing whether two events are independent?
Signup and view all the answers
What can be said about the relationship between the probabilities of two mutually exclusive events?
Signup and view all the answers
What is the purpose of the complementary rule?
Signup and view all the answers
What is the probability of the union of two mutually exclusive events A and B?
Signup and view all the answers
If two events A and B are independent, what is the probability of A and B not occurring?
Signup and view all the answers
What is the formula for the probability of an event A not occurring?
Signup and view all the answers
What is the term for the set of all possible outcomes in a probability experiment?
Signup and view all the answers
If A is an event, what is the notation for the number of elements in set A?
Signup and view all the answers
What is the formula for the probability of two independent events A and B occurring?
Signup and view all the answers
What is the relationship between the probability of an event A and its complement A'?
Signup and view all the answers
If two events A and B are mutually exclusive, what is the probability of their intersection?
Signup and view all the answers
If events A and B are mutually exclusive, what is the value of P(A or B) in terms of P(A) and P(B)?
Signup and view all the answers
What is the condition for the addition rule to hold for any two events A and B?
Signup and view all the answers
If P(A) = 0.3 and P(B) = 0.5, and A and B are independent, what is P(A and B)?
Signup and view all the answers
If A and B are dependent, what can be said about P(A and B)?
Signup and view all the answers
What is P(not A) in terms of P(A)?
Signup and view all the answers
If P(A or B) = 0.7 and P(A) = 0.4, what is P(B) if A and B are mutually exclusive?
Signup and view all the answers
What is the relationship between P(A) and P(not A)?
Signup and view all the answers
If A and B are independent, what is P(A and not B) in terms of P(A) and P(B)?
Signup and view all the answers
If two events A and B are independent, which of the following is true?
Signup and view all the answers
What is the probability of the union of two events A and B, if they are mutually exclusive?
Signup and view all the answers
What is the relationship between the probability of an event A and its complement A'?
Signup and view all the answers
If P(A) = 0.4 and P(B) = 0.3, what is the probability of A and B not occurring, if they are independent?
Signup and view all the answers
What is the term for events that are mutually exclusive and make up the whole sample space?
Signup and view all the answers
If A and B are mutually exclusive, what is the value of P(A and B)?
Signup and view all the answers
What is the purpose of the product rule?
Signup and view all the answers
What is the symbol for the number of elements in set A?
Signup and view all the answers