Stats 3.2 Conditional Probability and the Multiplication Rule

Multiplication rule

A rule of probability stating that the probability of two or more independent events occurring together can be determined by multiplying their individual probabilities.

When is an event unusual?

An event is considered unusual if its probability is less than or equal to 0.05

List an example of two events are dependent:

Drawing one card from a standard​ deck, not replacing​ it, and then selecting another card

T/F If two events are​ independent, ​P(A|B) = P(B)

False; if events A and B are​ independent, then​ P(A and ​B)= ​P(A) * ​P(B).

List an example of two events that are independent

Rolling a dice

Explain how the complement can be used to find the probability of getting at least one item of a particular type.

The complement of​ "at least​ one" is​ "none." So, the probability of getting at least one item is equal to 1 - P(none of the​ items).

Conditional Probability

The probability of an event occurring, given that another event has already occured. The conditional probability of event B occurring, given that event A has occurred, is denoted by P(B | A) and is read: "Probability of B, given A"

For the given pair of​ events, classify the two events as independent or dependent. Waking up and finding the alarm clock blinking 12 : 00 Getting to class late

The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.

independent

Two events are are independent when the occurence of one of the events does not affect the probability of the occurrence of the other event. Two events A and B are independent when: P (B | A) = P(B)

An example of dependent events

When drawing two cards​ (without replacement) from a standard​ deck, the outcome of the second draw is dependent on the outcome of the first draw.