SECTION 11-2 Events Involving “Not” and “Or” Slide

EVENTS INVOLVING “NOT” AND “OR” Properties of Probability Events Involving “Not” Events Involving “Or” Slide

PROPERTIES OF PROBABILITY Slide Let E be an event from the sample space S. That is, E is a subset of S. Then the following properties hold. (The probability of an event is between 0 and 1, inclusive.) (The probability of an impossible event is 0.) (The probability of a certain event is 1.)

EXAMPLE: ROLLING A DIE Slide When a single fair die is rolled, find the probability of each event. a) the number 3 is rolled b) a number other than 3 is rolled c) the number 7 is rolled d) a number less than 7 is rolled

EXAMPLE: ROLLING A DIE Slide Solution The outcome for the die has six possibilities: {1, 2, 3, 4, 5, 6}.

EVENTS INVOLVING “NOT” Slide The table on the next slide shows the correspondences that are the basis for the probability rules developed in this section. For example, the probability of an event not happening involves the complement and subtraction.

CORRESPONDENCES Slide Set TheoryLogicArithmetic Operation or Connective (Symbol) ComplementNotSubtraction Operation or Connective (Symbol) UnionOrAddition Operation or Connective (Symbol) IntersectionAndMultiplication

PROBABILITY OF A COMPLEMENT Slide The probability that an event E will not occur is equal to one minus the probability that it will occur. S So we have E and

EXAMPLE: COMPLEMENT Slide When a single card is drawn from a standard 52-card deck, what is the probability that it will not be an ace? Solution

EVENTS INVOLVING “OR” Slide Probability of one event or another should involve the union and addition.

MUTUALLY EXCLUSIVE EVENTS Slide Two events A and B are mutually exclusive events if they have no outcomes in common. (Mutually exclusive events cannot occur simultaneously.)

ADDITION RULE OF PROBABILITY (FOR A OR B ) Slide If A and B are any two events, then If A and B are mutually exclusive, then

EXAMPLE: PROBABILITY INVOLVING “OR” Slide When a single card is drawn from a standard 52-card deck, what is the probability that it will be a king or a diamond? Solution

EXAMPLE: PROBABILITY INVOLVING “OR” Slide If a single die is rolled, what is the probability of a 2 or odd? Solution These are mutually exclusive events.