Math 8 Unit 1 Probability Fall 2008
References Helpful Links: http://www.edhelper.com/mat h/probability6.htm http://www.mathgoodies.com/l essons/vol6/independent_eve nts.html http://regentsprep.org/Regent s/math/tree/Ltree.htm http://www.usca.edu/Free/mm p_counting/tree_diagrams.ht ml http://regentsprep.org/Regent s/math/counting/Lcount.htm http://www.edhelper.com/mat h/probability1.htm
Volume 1 Issue 1
Dear Parents Below you will find a list of concepts that your child will use and understand while completing Unit 1 Probability. Also included are references, vocabulary and examples that will help you assist your child at home.
Concepts Students will Use and Understand • • • •
Use tree diagrams to determine the number of outcomes to events. Understand outcomes of simple and compound independent events. Understand the counting principal to determine outcomes of events using addition and multiplication. Understand the laws of probability.
Vocabulary Independent events: Events for which the occurrence of one has no impact on the occurrence of the other. Relative frequency: The number of times an outcome occurs divided by the total number of trials. Sample space: All possible outcomes of a given experiment.
Mathematics Course 3 Textbook Connection : Chapter 10, Lessons: 1, 4, 5, 8
Event: A subset of a sample space. Simple Event: An event consisting of just one outcome. A simple event can be represented by a single branch of a tree diagram. Compound Event: A sequence of simple events.
Mathematics Course 3 Textbook Online: http://go.hrw.com/resource s/go_mt/hm3/so/c3ch10as o.pdf http://go.hrw.com/resource s/go_mt/hm3/so/c3ch10bs o.pdf
Complement: The complement of event E, sometimes denoted E′ (E prime), occurs when E doesn’t. The probability of E′ equals 1 minus the probability of E: P(E′) = 1 – P(E). Counting Principle: If an event A can occur in m ways and for each of these m ways, an event B can occur in n ways, then events A and B can occur in m gn ways. This counting principle can be generalized to more than two events that happen in succession. So, if for each of the m and n ways A and B can occur respectively, there is also an event C that can occur in s ways, then events A, B, and C can occur in ways. Tree diagram: A tree-shaped diagram that illustrates sequentially the possible outcomes of a given event.
Math 8 Unit 1 Probability Symbols
Example 1
P(A): probability of A
Use a tree diagram to determine the possible meal combinations given the following choices:
P(A or B):P(A)+P(B)
3 entrees 5 drinks 2 desserts
P(A and B): P(A)¡P(B) A′ - complement of event A
Example 2 Links
A jar contains 12 quarters and 4 nickels. What is P(quarter then nickel) if you select the first coin and replace it before your draw the second coin?
http://www.mathgoodies.c om/lessons/vol6/intro_pro bability.html
Example 3 1) If A and B are independent events such that P(A)= 0.50 and P(B)=0.25. A) What is the probability that both A and B will occur? B) What is the probability that both A or B will occur?
http://go.hrw.com/hrw.nd/g ohrw_rls1/pKeywordResul ts?keyword=MT7+Parent
Key Example 1 30 Example 2
12 3 4 = . Since you replace the first coin the P(nickel)= because there are still 16 16 4 16 3 4 12 3 = coins in the jar. The P(quarter then nickel)= g = 4 16 64 16 P(quarter)=
Example 3
A)
P(A)= 0.50 and P(B)=0.25 so the P(A and B)=
0.50g0.25 = 0.125
P(A)= 0.50 and P(B)=0.25 so the P(A or B)= 0.50 + 0.25 = 0.75