MATH HOMEWORK CASE, SLP and THREAD DISCUSSION

Module 1 - Home

Introduction to Probability

Modular Learning Outcomes

Upon successful completion of this module, the student will be able to satisfy the following outcomes:

•Case

◦Identify the meaning of independent and dependent variables.

◦Calculate probabilities and joint probabilities of simple events.

◦Explain the basic logic of probability theory.

•SLP

◦Explain the basic logic of probability theory.

◦Identify the meaning of independent and dependent variables.

•Discussion

◦Explain the basic logic of probability theory.

◦Define the meaning of probability.

Module Overview

Types of descriptive statistics:

•N = Count. The number of cases (people, companies, plants, or whatever is being analyzed)

•Sum(X) = The "added-up" value of the variable X, for all the cases.

•Mean(X) = The mean, or average value of the variable X, over all the cases. Mean(X) = Sum(X)/N.

•Median(X) = The "middle value" of X. This is found by sorting the data from small to large, and finding the value that appears midway between small and large. If N is an even number, the median is the mean value of the two "middle values."

•Mode(X) = The value of X that appears most frequently in the list. There may not be a mode if the values of the data don't repeat.

•SD(X) = The standard deviation of X. This is a measure of how "spread out" the data are.

The probability of some outcome is the number of times the outcome occurs, divided by the number of possible outcomes, both expected and not expected. Probability is a positive number between 0 and 1.00. Examples:

•The probability of flipping a coin and getting heads = 1/2 = 0.50.

•The probability of drawing a spade from a deck of shuffled cards = 13/52 = 0.25

•The probability of drawing an ace from a deck of shuffled cards = 4/52 = 0.07 (approx.)

•The probability of drawing the Queen of Spades from a deck of shuffled cards = 1/52 = 0.02 (approx.)

A conditional probability is the probability of a particular outcome, given that a prior outcome has occurred. Examples:

•The probability of drawing an ace, given than a black card was drawn = 2/26 = 0.07 (approx.)

When estimating a conditional probability from a list of outcomes, simply count the number of prior outcomes, and divide by the number of subsequent outcomes. Example: What is the probability of outcome A, given outcome 1?

CASE	FIRST OUTCOME	SECOND OUTCOME
1	1	A
2	2	A
3	1	B
4	2	B

In cases 1 and 3 the first outcome = 1. Of those two, only one case (1) has a second outcome of A. Therefore, the chance of A given 1 is 1/2 = 0.50.