Venn Diagrams.

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Presentation transcript:

Venn Diagrams

A Venn Diagram is a useful way of showing the relationship between events. For example, we have the events E, F and G and the sample space U. See if you can determine the following relationships given by the shaded region. U shaded region:

U shaded region:

U shaded region:

U Relationship:

shaded region:

shaded region:

shaded region:

U F E shaded region:

U E F shaded region:

If A and B are two events given the following: Find: Answer: a) b) Answer:

If A and B are two events such that find P(A). Answer: 0.5

Events X and Y are such that find: Answer:

Events X and Y are such that find: Answer:

A country club has 100 members, 30 of whom are lawyers A country club has 100 members, 30 of whom are lawyers. Rumor has it that 25 of the club members are liars and 55 are neither lawyers nor liars. What proportion of the club are liars but not lawyers? Answer: 15 members

One hundred students attended at least one of three concerts: Pep Band, Country Sizzle, and Blue Mood. 48 heard the Pep Band concert. 36 heard the Country Sizzle concert. 60 heard the Blue Mood concert. 12 heard the Pep Band and Country Sizzle concerts. 20 heard the Country Sizzle and Blue Mood concerts. 16 heard the Pep Band and Blue Mood concerts. How many attended all three concerts? Answer: 4 students

From a small town 120 persons were selected at random and asked the following question: Which of the three shampoos, A, B or C, do you use? The following results were obtained: 20 use A and C, 10 use A and B but not C, 15 use all three, 30 use only C, 35 use B but not C, 25 use B and C and 10 use none of the three. If a person is selected at random from this group, what is the probability that he or she uses (a) only A; (b) only B; (c) A and B?