Notes 6.2: Venn Diagrams - Mrs. Bogues' Classroom
Learning Target Using Venn Diagrams in probability situationsVenn Diagram: Models the probability of events and sample spaces.The diagrams help to visually solve probability without using formulas and make it easy to determine if there is overlap between events. Sometimes Venn Diagrams are done using whole numbers (and you can use these to compute probabilities) and sometimes they are done with probabilities (in percent, fractions or decimals).Example 1: Sketch a Venn Diagram that shows the following events.Disjoint (no overlap)Joint (overlap) Complement of A (Ac)? I can use Venn Diagrams to visualize and determine P(A or B) ?A or B is called union and can be written as A ∪ B. Union represents combined data.OR = UnionIf disjoint, then P(A or B) = P(A) + P(B)If joint, then P(A or B) = P(A) + P(B) – overlap = P(A) + P(B) – P(A and B)Example 1: 50 students are in band and 45 students are in choir. 25 students are in both band and choir. Draw a Venn diagram to determine the number of student in band or choir.? I can use Venn Diagrams to visualize and determine P(A and B) ?A and B is called intersection and can be written as A ∩ B. Intersection represents the overlap.AND = Intersection If A and B are independent, then P(A and B) = P(A)·P(B)Example 2: Donald ordered a computer and a desk from two different stores. Both items are to be delivered on Tuesday. The probability that the computer will be delivered before noon is 0.6 and the probability that the desk will be delivered before noon is 0.8. These deliveries are independent of each other. Determine the probability that the desk and computer are both delivered before noon using a Venn Diagram.? I can use Venn Diagrams to visualize and determine P(B|A) ?To find P(B|A), look at only A (this is your total). Then determine the part of B that is also in set A.Example 3: An instructor recommended 50 students take calculus and 45 take statistics. Of these students, 15 students were recommended to take both calculus and statistics at the same time during their first year of college. Draw a Venn DiagramFind P(Calculus | Statistics)Find P(Statistics | Calculus) ................
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