## Video Links 13-4

**Video:**

Independent events; probability of an intersection (time: 8:03)

Tree diagrams (time: 6:07)

… See the whole entry

**Video:**

Independent events; probability of an intersection (time: 8:03)

Tree diagrams (time: 6:07)

… See the whole entry

**Problems 1-6**

Use the tree diagram to find each requested probability. See Example 1.

**Problem 7-12**

Use a tree diagram and Bayes’ theorem. See Example 4.

**Problem 13-24**

Use the Venn diagram and look for the given set. See Example … See the whole entry

**Problem 1**

Look in the book to find a statement of this term.

**Problems 2-3**

Make sure you know these formulas, as well as the conditions for which each applies.

**Problem 4**

Look in the book to find a statement … See the whole entry

- Keno games
- Independent events
- independent
- dependent

- Probability of an intersection
- multiplication property of probability
- birthday problem

- Probability of a union
- addition property of probability
- probability of independent events

- Drawing with and without replacement
- Stochastic processes and tree diagrams

- Election problem
- tree diagram
- fundamental counting principle
- arrangement
- ordered pair/ordered triple
- define permutation
- notation for permutations
- evaluating permutations

- Factorial
- definition
- multiplication property of factorials
- count-down property
- permutation formula

- Distinguishable permutations
- indistinguishable items
- distinguishable items
- formula for distinguishable permutations

Prepare a classroom demonstration of topology by drawing geometric figures on a piece of rubber inner tube. Demonstrate to the class various ways in which these figures can be distorted.

The problem shown in the News … See the whole entry

**Videos:**

Kruskal’s Algorithm (time: 2:40)

This is a rather foolish introduction to spanning trees (time: 1:39)

… See the whole entry

A historical reference, along with a solution and interesting links for the Konigsberg bridge problem is found at this site:

https://maa.org/press/periodicals/convergence/leonard-eulers-solution-to-the-konigsberg-bridge-problem

This site provides a nice discussion of minimum spanning trees.

http://www.people.vcu.edu/~gasmerom/MAT131/mst.html

This is a nice interactive demonstration of Krukal’s … See the whole entry

**Problems 1-4**

There questions are basically definitions and procedures. Read the book and then paraphrase each in your own words.

**Problems 5-12**

Review the definition of a tree and see Examples 1 and 2.

**Problems 13-20**

Review the definition of … See the whole entry

- Trees
- definition
- spanning tree

- Minimum spanning trees
- weight
- weighted graph
- definition
- Kruskal’s algorithm
- number-of-vertices-and-edges-in-a-tree theorem

A **tree** is a graph which is connected and has no circuits. A tree that is created from another … See the whole entry