Two way tables & venn diagrams
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Students in a college statistics class collected data on 178 students' gender and whether their ears were pierced. They recorded this information in a two-way table to calculate probabilities. The two-way table showed that of the 90 male students, 19 had pierced ears. Of the 88 female students, 84 had pierced ears. The probabilities of being male with pierced ears, having pierced ears, or being male or having pierced ears can be determined from this two-way table.
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Two way tables & venn diagrams
- 1. Two-Way Tables • When finding probabilities involving two events, a two-way table can make the calculations easier. College statistics students wanted to find out how common it is for young adults to have their ears pierced. They recorded data on two variables – gender and whether the student had pierced ears, for all 178 people in the class. If we choose a student at random, Gender What is the probability that Male a. They have pierced ears Female b. They are male with pierced ears TOTAL c. They are male or have pierced ears Pierced Ears Yes No TOTAL 19 71 90 84 4 88 103 75 178
- 2. Venn-Diagrams • If events A and B are not mutually exclusive, they can occur together • The probability that one or the other occurs is less than the sum of their probabilities
- 3. Venn-Diagrams • A Venn diagram takes of the double counting problem using the General Addition Rule of Two Events: P(A or B) = P(A) + P(B) – P (A and B) If two events are mutually exclusive, the P(A and B) = 0 - This is just a special case of the addition rule since P(A and B) = 0, we are subtracting nothing P(A or B) = P(A) + P(B)
- 4. Venn-Diagrams Vocabulary and Standard Notation: • The complement of an event AC contains the outcomes that are not in A • Events A and B are mutually exclusive (disjoint) if they do not overlap, that have no outcomes in common.
- 5. Venn-Diagrams Vocabulary and Standard Notation: • The event A and B is the intersection of A and B, and it is notated as A∩B • The event A or B is the union of A and B, and it is notated as AUB
- 6. Venn-Diagrams The notation that will be used on the AP Exam that is also on the equation sheet: P(A U B) = P(A) + P(B) – P(A ∩ B) or and • A U B represents union (or) • A ∩ B represents intersection (and) Pg. 306-307