Section 2 Probability Rules – Compound Events

Compound Event – an event that is expressed in terms of, or as a combination of, other events Events A and B are independent if the occurrence of one has no effect on the probability of the occurrence of the other.

Multiplication Rule for Independent Events P(A and B) = P(A)∙P(B) Example If you roll two dice, what is the probability you get a 5 on each die?

Multiplication Rule for Dependent Events P(E and F) = P(E) ∙ P(F/E) Conditional Probability notation P(F/E) “the probability of event F given event E” the probability of an event F occurring given the occurrence of the event E.

Example A bag contains five red marbles, two blue marbles, and seven yellow marbles. What is the probability that if two marbles are randomly chosen, the first is red and the second is blue?

Events A and B are mutually exclusive events if they cannot both occur together when the experiment is performed. Addition Rule for Mutually Exclusive Events P(A or B) = P(A) + P(B)

Example Find the probability of drawing a spade or a heart from a standard deck of cards.

Addition Rule P(A or B) = P(A) + P(B) – P(A and B) Example Find the probability of drawing a king or drawing a diamond from a standard deck of cards.

Conditional Probability P(E and F) = P(E) ∙ P(F/E) P(E) P(E) P(F/E) = P(E and F) P(E)

Example At a small company, six of the ten employees are computer programmers. Five are female and two are female computer programmers. If an employee is selected by chance, what is the probability that: A.) the employee is a computer programmer, given that the employee is female B.) the employee is female, given that the employee is a computer programmer