Addition RuleMr. Evans

Statistics B

Venn Diagram

• It is often possible to illustrate the various sets or events of an experiment. For this we use Venn Diagrams. • In a Venn Diagram a rectangle is drawn to represent the sample space S.

• Then all the possible outcomes of a random experiment are contained at points within the rectangle.

• If we represent two events A and B by circles such that all the elements of A and B respectively are contained within the circles, we can illustrate a number of combined events.

• Some common events are illustrated and defined in the table on the next slide

Venn Diagrams

Compound Events

• Compound Event is any event combining 2 or more simple events• P(A or B) = P(event A occurs or event B occurs

or they both occur)

Mutually Exclusive

• Two event, A and B, are mutually exclusive if they cannot occur at the same time.

Guided Exercise #1

Decide if the 2 events are mutually exclusive.

 

• Event 1: Roll a number less than 3 on a die.

• Event 2: Roll a 4 on a die.

 

• Event 1: Select a Jack from a deck of cards.

• Event 2: Select a heart from a deck of cards.

Mutually Exclusive

Not Mutually Exclusive

The Addition Rule

• The probability that event A or B will occur is given by• P(A or B)=P(A)+P(B)-P(A and B)  

• If events A and B are mutually exclusive, then the rule can be simplified to  • P(A or B)=P(A)+P(B)

Guided Exercise #2

Find the probability that you roll a number less than 3 or a 4.

A card is randomly selected from a deck of cards. Find the probability that the card is a Jack or the card is a heart.

Roll 1 or 2 Roll 4

Jacks HeartsJack of Hearts