L ESSON 13.2 Counting the Elements of Sets Throughout this lesson, you only need to copy things that are typed in orange!

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Presentation transcript:

L ESSON 13.2 Counting the Elements of Sets Throughout this lesson, you only need to copy things that are typed in orange!

“AND” The INTERSECTION of two sets consists of the elements that are common to both sets. The symbol is used.

“OR” The UNION of two sets consists of the elements of both sets. The symbol is used.

“ DISJOINT ” When the two outcome sets from a sample space do not overlap, they are said to be disjoint.

C OUNTING ELEMENTS OF SETS Suppose that there are m elements in set M and n elements in set N; then the total number of elements in the two sets is m+n-t, where t is the number of elements in the intersection of M and N.

In a card game called Crazy Eights, if the queen of hearts is showing, you can play only a queen, a heart, or an eight. How many different cards can be played in this situation assuming that all cards except the queen of hearts are available? (52 cards in a deck, 4 suits, each suit has 13 cards – A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K) Answer: Do not count the queen of hearts (it has already been played). There are 3 other queens, 12 other hearts, and 4 eights – with the eight of hears being counted twice. Thus, there are – 1, or 18 cards that can be played.

If you draw a card at random from a complete deck of 52 playing cards, what is the probability that you will draw a king? What is the probability that you will draw a queen? What is the probability you will draw a kind OR a queen? There are 4 kings and 4 queens in the deck. P(king) = 4/52 = 1/13. P(queen) = 4/52 = 1/13. Since there are 8 cards in the set of favorable outcomes for drawing a king or a queen, the probability is as follows: P(king OR queen) = 8/52 = 2/13

A DDITION OF P ROBABILITIES P RINCIPLE If M and N are intersecting sets of outcomes in the sample space, then P(M OR N) = P(M) + P(N) – P(M N). If M and N are disjoint sets of outcomes in the same sample space, then P(M OR N) = P(M) + P(N).

What is the probability of drawing a face card or a spade from a deck of playing cards? There are 12 face cards and 13 spades. Three of the 13 spades are also face cards, so there are 3 cards in the intersection of the two sets. Let F be the set of face cards and S be the set of spades. P(F or S) = P(F) + P(S) – P(F intersect S) 12/ /52 – 3/52 = 22/52 = 11/26

List the integers from 1 to 10 inclusive that are 1. Even 2. Multiples of 3 3. Even AND multiples of 3 4. Even OR multiples of 3 {2, 4, 6, 8, 10} {3, 6, 9} {6} {2, 3, 4, 6, 8, 9, 10}

Favor RuleOppose RuleTotal Boys4913 Girls71017 Total Mark took a class survey to get student opinions about a new rule concerning students driving to school. Use the table to answer the questions. (Please copy the chart into your notes!) 1.How many of those surveyed are boys? 2.How many are girls AND oppose the rule? 3.How many are girls OR oppose the rule? 4.How many are boys AND favor the rule? 5.How many are boys OR favor the rule?

Please get a homework sheet from the substitute teacher. You must do ALL of the problems on the worksheet!