11.6 Probabilities Involving NOT and OR

Problem 1

Imagine throwing a die. What is the probability of getting a 2?

What is the probability of not getting a 2?

Probability of an Event NOT occurring (a.k.a. P (NOT) )The probability that an event E will not occur is equal to 1 minus the probability that it will occur

P (not E) = 1 – P (E)

Sample Problems (# 2)If you throw a die, what is the

probability of not getting an even number?

If you are dealt one card from a standard 52-deck card, what is the probability of not getting◦A king?◦A heart?◦A picture card?

Problem # 3

Assume that it is equally probable that the pointer will land on any one of the five numbered spaces.

Find the probability of not getting a 2

Find the probability of not getting an odd number

ODDSOdds in favor of an event = P (E) P (not E)

Odds against E = P (not E) P (E)

Note: Odds in favor and odds against are reciprocals.

Sample Problems (#4)

In a standard 52-deck card, a. Find the odds in favor of getting

a kingb. Find the odds against getting a

diamondc. Find the odds in favor of getting

a black aced. Find the odds against getting a

red picture card

Sample Problems (# 5)If you toss 2 coins together, the

possible outcomes are {HH, HT, TH, TT}

Find the odds in favor of getting two heads

Find the odds against getting a head and a tail.

Odds to ProbabilityIf the odds in favor of event E are

a to b, then the probability of the event is

P(E) = a a + bExample: The odds in favor of

winning a horse winning a race are 2 to 5. What is the probability that the horse will win?

Probabilities Involving OR

Mutually exclusive events – events that occur simultaneously

If A and B are mutually exclusive events, then P(A or B) = P (A) + P(B)

Example: In a standard 52-deck card, what is the probability of getting a king or a queen?

Sample Problems (# 6)If you roll a single die, what is the

probability of getting:a. 3 or a 5b. A number less than 3 or number

greater than 4

Probabilities Involving OR What if the events are not mutually

exclusive?

OR Probabilities with events that are not mutually exclusive

If A and B are not mutually exclusive, then P(A or B) = P(A) + P(B) – P (A and B)

Suppose you’re asked to pick a card from a standard 52-deck card. What is the probability of getting a king or a diamond?

Sample Problems (# 7)Assume that it is equally

probable that the pointer will land on any one of the five numbered spaces.

a. What is the probability of getting a number greater than 2 or an odd number?

b. What is the probability of getting an odd number or a number less than or equal to 3?

AssignmentClass work: pages 601-602, #s 5,

9, 15, 23, 33

HW: pages 601-603, #s 2-66 (even)