Two events are called to be independent events if the occurrence or non-occurrence of one event does not affect the probability of the other event.

If A and B are independent events, the probability of both events A and B occurring is the product of their individual probabilities:

P(A and B) = P(A) * P(B)

With this, we can simplify tree diagrams when dealing with problems with multiple same items by simply marking their probabilities.

When two (or more) events are dependent to each other, we cannot use the product rule, but we can still use the tree diagrams to help us finding probabilities.

Homework:

Print these pages (pages are links. Click to download): Page 1, Page 2, Page 3

Workbook Page 12, #6, #7, #10, #16, #19, #20.

We start on probability. Students should have learned some basic concepts before about simple probability, the concept of a sample space with events consisting of some outcomes. In this chapter ,we study probabilities with multiple stages.

When a random experiment involves two stages, we can use a rectangular grid, called a probability diagram, to represent the sample space to help us find probabilities.

If a random experiment has two or more stages, we can use a tree diagram to represent the process, which should help us see all the possible outcomes and figure out the outcomes associated with a particular event.

We then talk about mutually exclusive events. In a sample space, two events are mutually exclusive if they cannot occur at the same time. If A and B are two mutually exclusive events, the the probability of A or B occurring is: P(A or B) = P(A) + P(B).

Note, there is no class next Thursday 10/13 following school’s calendar

Homework:

Print these pages (pages are links. Click to download): Page 1, Page 2

Workbook Page 11, #1 – #5, #21.

We continue study of standard deviation.

We apply the standard deviation to help analyze two data sets. While means can give us the picture of average, standard deviation helps us to determine how consistent the data are. For example, if we look at two sets of data representing two basketball players’ scores, the lower the standard deviation, the more consistent the player is.

Homework:

Print these pages (they are links, click to download): Page 1, Page 2, Page 3

Workbook Page 1, 2, 3: #10, 12, 14, 16.

We continue study of standard deviation. Today we study standard deviation for grouped data.

We talk about the formulae for grouped data.

Homework:

Print these pages (they are links, click to download): Page 1,  Page 2, Page 3, 

Workbook Page 1, 2, 3: #2, #3, #7, #8, #9

We study standard deviation. In statistics, we have learned using mean to find the average, and we have learned to use range to see the spread of the data. But range is not very good as the tool to represent the spread of the data.

A better way is the measure called standard deviation:

Standard Deviation SD = sqrt(sum of (Xi – AvgX)^2/N)

where N is the total number of data, AvgX is the mean of the data. Xi – AvgX is called the deviation of Xi from the mean AvgX for each i = 1, 2, …, N

[Sorry, I can’t type using the summation notation sigma, which is what we learn in the class. This will simplify the writing.]

Here is a written proof of going from the definition to a formulae often used:

sqrt(∑(Xi – AvgX)^2 / N) = ∑Xi^2 / N – (∑Xi / N)^2

I showed the proof in the classroom, but students may not get it.

Homework (pages are links, click to download):

Page 1  and Page 2: #1, #4, #5, #6.