Objectives: Find the union and intersection of sets. Count the elements of sets. Apply the Addition of Probabilities Principle. Standard Addressed: D: Use theoretical probability distributions to make judgments about the likelihood of various outcomes in uncertain situations Counting the Elements of Sets

In a Venn Diagram, circles are used to represent sets. When circles overlap, the overlapping region is known as the intersection of the sets. The intersection of two sets consists of the elements that are common to both sets. The logical relationship AND represents the intersection of two sets. The intersection of sets is shown by the symbol n. The intersection of sets M and N is written as (M n N). The logical relationship OR represents union of sets. The union of two sets consists of all elements of both sets. In a Venn diagram of the union of two sets, the whole circles are shaded. The union of two sets is shown by the symbol U. The union of sets M and N is written as (M U N).

Ex. 1a.

Ex 1b. How many cards in a deck of playing cards are spades OR aces? 13 cards are spades and 4 cards are aces but 1 card is both and shouldn’t be counted twice 16 cards total

Ex. 2a. Disjoint ---- ME 4 kings and 4 queens in a deck P (king OR queen) = 4/52 + 4/52 = 8/52 =2/13

Ex. 2b. If you draw a card at random from a complete deck of 52 playing cards, what is the probability that you will draw a spade OR a club? Disjoint --- ME P(spade OR club) = 13/ /52 = 26/52 = 1/2

Ex. 3a.

b. What is the probability of drawing an odd-numbered spade OR an ace from a deck of playing cards? (Note: The numbered cards are ace through 10 in each of the four suits; an ace counts as one.) P (odd # spade OR ace)= 8/52 =.15

Ex 4a. ME --- DISJOINT P (oppose OR no opinion) = 37/ /100 = 73/100 = 73%

Ex 4b. I --- Intersecting P (man or opposes) = 50/ /100 – 12/100 = 75/100 = 75%

Summary of Relationships Between Two Sets INTERSECTIONUNIONDISJOINT