Probability: Inclusion-Exclusion Principle
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- Principles of Inclusion and Exclusion Let's say we are trying to count the number of students in a class. The only data we have is that everyone in the class plays a sport. 1212…
By Ben Ferrara, Ishwar Karthik, Alex Federspiel, Michelle Newstadt, Joshua Siktar
- Inclusion-Exclusion Principle Before we get to practice word problems using the inclusion-exclusion principle, it might help to see what the principle looks like in a picture. W…
By Hannah Bonville, Alex Federspiel, Joshua Siktar
- Introduction Before we get started let's have a brief review of Venn diagrams. Venn diagrams are those circle things that overlap. Remember? Set AAA is the left circle, set BBB …
By Alex Federspiel, Victoria Rodriguez, Joshua Siktar
- (Video) Ch9Pr4: Inclusion/Exclusion Principle by MathsStatsUNSW In this video, we walk through a problem that uses the inclusion-exclusion principle. Summary\large{\text{Summary…
By Amy Feraco
Problems 19
- How many integers are there from 555 to 60,60,60, exclusive (excluding 555 and 606060)?
- A kindergarten teacher asks her kids who likes what kind of ice cream. 666 liked vanilla, 555 liked chocolate, 333 liked strawberry. If 333 kids like all three flavors, how many…
- True or False\text{True or False}True or False === A Venn Diagram is a good way to accurately show two sets of data that have overlapping points.
- A group of students was asked to put a sticker in the Venn Diagram. Which statement matches the above?
- In a class, 171717 students had at least one brother; 181818 students had at least one sister; 666 students had at least one brother and one sister; 555 students had neither a b…
- A binary string is an ordered collection of digits that are all 000s or 111s. How many binary strings of length 101010 begin with three 000s or end with two 000s?
- Recorded above are the results of a survey of 303030 people who were asked whether or not they liked sunrises, and also whether or not they liked sunsets. 131313 like sunrises, …
- Consider this equation: n(A∪B)=n(A)+n(B)−n(A∩B).n(A \cup B) = n(A) + n(B) - n(A \cap B).n(A∪B)=n(A)+n(B)−n(A∩B). What does the ∪\cup∪ represent?
- Which of the following correctly represents the situation where we have sets A,B,A, B,A,B, and CCC intersecting three ways with each other?
- Everyone who uses expii wants to learn. 141414 users say they wanted to learn Geometry, 191919 users said they wanted to learn Biology and 555 said they wanted to learn both. Ho…
- 404040 people were surveyed as to whether they like cake or ice cream. 202020 people like ice cream, 202020 like cake, and 101010 like both. Using the information given, determi…
- 100100100 athletes at Washington high school were surveyed and asked whether they participate in track or field. 212121 said field, and 101010 said both. How many athletes were …
- What does ∩\cap∩ represent in the inclusion-exclusion formula? For reference, this formula is n(A∪B)=n(A)+n(B)−n(A∩B).n(A \cup B) = n(A) + n(B) - n(A \cap B).n(A∪B)=n(A)+n(B)−n(…
- 505050 consumers were surveyed and asked whether or not they like grape flavored cough medicine, orange flavored cough medicine, or both. If 151515 people like grape flavored co…
- Andrew decided to run a simulation to find the probability of him being late for work. He decided to determine this by considering the probability of two events. Event A: He get…
- A survey asking 505050 people about the languages they speak was conducted. 444444 speak English, 242424 speak Spanish Allow Event A to be the case that someone speaks English a…
- A survey asking 100100100 people about which genre of music they listen to was conducted at random. The results are shown above. \\ Allow Event AAA to be the case that someone e…
- Which of the following is not an application of the inclusion-exclusion principle?
- Which of the following formulas will successfully count the number of elements in the union of three sets?