Events Involving NOT and OR, Odds

​Probability of an Event NOT occuring

P(E) + P(not E) = 1

​The event not E is the COMPLEMENT of E because it is the set of all outcomes in the sample space S that are not outcomes in the event.

The complement rule of probability is

P(not E) = 1 - P(E)

P(E) = 1 - P(not E)

​If you are dealt one card from a standard 52 card deck, find the probability that you are not dealt a queen.

​Because P(not E) = 1-P(E)

Then P (not a queen) = 1 - P(queen)

4/52 = 1/13 1 - 1/13 = 13/13 - 1/13 = 12/13

​If it is impossible for events A and B to occur simultaneously, the events are said to be Mutually Exclusive

​P(A or B) = P(A) + P(B)

P ( A U B) = P(A) + P(B)

​If one card is randomly selected from a deck of cards what is the probability of selecting a king or queen?

​P (King or Queen) = P(King) + P(Queen)

4/52 + 4/52 = 8/52 = 2/13

​If A and B are not mutually exclusive then

P(A or B) = P(A) + P(B) - P(A and B)

Using set notation

P(A U B) = P(A) + P(B) - P (A ⋂ B )

​You roll a single number cube

a. Find the odds in favor of rolling a 2

b. Find the odds in favor against rolling a 2

a. b.