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:

Workbook Page 12, #6 – #10, #16 – #20.

We start a new subject 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).

Homework:

Workbook Page 11, #1 – #5, #21.

Today we review functions and graphs. We look at linear functions, quadratic functions, functions in the form of y = ax^n, where n = -2, -1, 0, 1, 2, and 3,  exponential functions y = ka^x, a > 0, and how to estimate the gradients of curves by drawing tangents.

Students should have learned these topics before and this is a review lesson to refresh their memories.

Homework: #1 – #12 from the pages below:

Page 1, Page 2, Page 3.