Venn Diagrams and Tree Diagrams
Venn diagrams and tree diagrams are fundamental tools used in various fields, including mathematics, statistics, and computer science, to visually represent relationships and organize information. Venn diagrams illustrate the overlap and distinctions between different sets or groups, showcasing the intersections and unions of elements. On the other hand, tree diagrams present hierarchical structures, depicting sequences of events or decisions in a branching format. Both diagrams serve as powerful aids in problem-solving, decision-making, and analyzing complex scenarios, offering clear visualizations that enhance understanding and facilitate effective communication.
Questions
- Help w/ Another Tree Diagram Question?
- Given the following survey results, how many people like C only?
- Can someone help me with this contingency table??
- For a Gallup poll, #M# is the event of randomly selecting a male, and #R# is the event of randomly selecting a Republican. Are events #M# and #R# disjoint? Why or why not?
- Friday night Joe decided to order a 1-topping pizza. He had a choice of thin or thick crust and a choice of five toppings. How many different pizzas could he choose from?
- If P(A)=1/4,P(B)=1/3 and P(A∪B)=1/2 find the values of 1. P(A∩B) 2. P(A∩B') 3. P(A'∩B') ?
- A basketball team plays 60% of its games at home. The home court advantage is obvious, because the team wins 70% of its home games, but when they play away, they win only 35% of their games. What is the (conditional) probability of losing, GIVEN THAT the game was played away?
- A basketball team plays 60% of its games at home. The home court advantage is obvious, because the team wins 70% of its home games, but when they play away, they win only 35% of their games. Create a tree diagram to illustrate the paths for home and away games and the outcome of winning or losing for each type of game.
- Of 200 students surveyed, 120 students liked Soda, 75 students liked juice, and 190 students liked soda or juice. How many students liked soda and juice?
- Please refer to the image here. ?
- A survey shows that 48% of the respondents like soccer, 66% like basketball, and 38% like hockey. If Meg likes basketball, what is the probability that she also likes soccer?
- What is the difference between mutually exclusive and independent events?
- If events are mutually exclusive are they independent?
- Three events A, B and C are defined in the sample space S. The events A and B are mutually exclusive and A and C are independent. What is #P(A|C)#?
- How do Venn diagrams and tree diagrams help you calculate probabilities?
- In a certain department, 45 students are enrolled in a chemistry class, 37 students are enrolled in biology, and 16 students are enrolled in both. Assuming every student is in at least one of the courses, how many students are enrolled in exactly one course?
- In a group of 50 patrons, 18 patrons like lattes, 16 patrons like espressos, and 8 patrons like both coffee drinks. How many patrons don't like either of the coffee drinks?
- For a custom car, there are 7 choices of wheel covers, 4 choices of stereos, 8 choices of colors, and 2 choices of windows. If you made a tree diagram to show all the possible outcomes, how many leaves would the tree diagram have?
- A company with 500 employees wants to have its group health insurance premiums lowered. Here is one question from the questionnaire that every employee filled out and returned to the HR department: What have you done in the past year to improve your health? (circle all that apply) A. I have eaten healthier. B. I have exercised regularly. When the results were tabulated, the HR clerk reported that 140 people circled response A, 290 circled response B, and 50 people circled both responses A and B. Given that a randomly selected individual answered B, what is the probability that he or she also answered A?
- Which two-way table contains the same information as the Venn diagram?