Download Unit 7 Study Guide

Probability & Geometry Study Guide
For the following scenarios create an area model and solve the probability questions
1.
2.
3.
You have 2 spinners one with 4 equal sections (red, white, blue, green) and one with 3 equal sections (red, blue, red)
a. If you spin both spinners what is the probability that both will land on red?
b. If you spin both spinners what is the probability of at least one red?
c. If you spin both spinners what is the probability that both colors will be the same?
d. If you spin both spinners what is the probability that the colors will not be the same?
You have a spinner with 4 equal sections (red, blue, green, red) and a standard die?
a. What is the probability of getting a blue 6?
b. What is the probability of getting an even number and green?
c. What is the probability of getting a red 3?
d. What is the probability of NOT getting a blue 3 or blue 4 in one spin/roll?
You have 2 standard 6 sided dice and finding the sum of each roll?
a. What is the probability of rolling a 7?
b. What is the probability of not rolling a 2 or 12 in one roll?
c. If you rolled the dice 100 times how many times would you expect to roll a 4?
d. If you rolled the dice 100 times how many times would you expect to not roll a 6?
e. What is the probability of rolling a 5 then rolling an 8?
For the following scenarios create a tree diagram and solve the probability questions
4.
5.
6.
You flip a coin 3 times
a. What is the probability of getting exactly 2 heads?
b. What is the probability of not getting a tail?
c. What is the probability of getting all 3 heads?
d. What is the probability of getting a heads, then tail, then heads?
You roll a die (1-6) spin a spinner with equal sections ( 1, 2, 3) and flip a coin (1, 2) and find the sum.
a. What is the probability of an even sum?
b. What is the probability of an odd sum?
c. What is the probability of a sum greater than 6?
d. What is the probability of a sum of 4?
For dinner your mom offers (tacos, burritos, fajitas) a choice of (Beans, rice, corn) and ( milk, or water)
a. How many different meals could you have?
b. What is the probability of having burritos and beans?
c.
What is the probability of not having milk?
d. What is the probability of having tacos?
Determine the number of possible outcomes
7.
8.
9.
10.
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16.
17.
If you have 8 students how many different ways can you line them up?
If you have 4 CD’s how many different ways can you listen to them?
How many 3 digit numbers can be made using digits 0-9 if the digits can repeat?
How many 3 digit numbers can be made using digits 0-9 if the digits cannot repeat?
Suppose there are two routes you can drive to get from Austin, Texas to Dallas, Texas, and four routes from Dallas, Texas to
Tulsa, Oklahoma. How many possible routes are there from Austin to Tulsa through Dallas?
In how many ways can 8 students enter a classroom?
Suppose you use five different letters from the 26 letters of the alphabet to make a password. Find the number of possible
five-letter passwords if letters cannot repeat.
Suppose a license plate consists of five different letters.
a. How many five-letter license plates are possible?
b. In how many ways can a five-letter license plate be made with the letters from APRIL if none of the letters are
repeated?
c. Suppose a license plate is assigned randomly. What is the probability that it will contain the letters from APRIL?
In how many ways can nine mopeds be parked in a row?
Suppose there are three different ways in which you could go from your house to a friend’s house. From your friend’s house,
there are four different ways in which you could go to the library. In how many different ways can you go from your house to
the library after meeting your friend?
Suppose you are electing student council officers. The student council contains 24 students. In how many ways can a president,
a vice president, and a secretary be elected?
18. A car dealer sells four different models of cars. Each of the cars can come in six different colors. For each of the cars, there
are two different option packages available. In how many different ways can you select a car?
19. Teams in a math competition consist of six students. In how many ways can the six students be selected to work a problem on
the board?
Figuring the total from a sampling
20. You have 1000 students at Hopewell and you take the following survey of 20 random students. 5 of them prefer vanilla ice
cream, 10 prefer chocolate, 3 prefer strawberry and 2 prefer sherbet.
a. Determine how many of the 1000 students prefer chocolate
b. Determine how many of the 1000 students prefer ice cream to sherbet.
21. There are 100 colored blocks in a box. You reach in and pull out 10 blocks. 4 red, 3 white, 2 blue , 1 green.
Based on your findings determine how many of the 100 blocks are
a. Red
b. White
c. Blue
d. Yellow
Set Notation
22. Based
c.
d.
e.
f.
g.
on the sets at the right
List 3 subsets of set A
List A  B
List A  B
List A 
Is 3  A ?
h. Is
2,3,4,6  A
Operations with Exponents
23. Simplify the following
i.
j.
k.
3a 2b  5a 3b 
2x 
2 3
4x 10
 6xy 5 2x 3y



Systems of Equations
24. Solve the following systems using any method
l.
m.
n.
5 x  2 y  4

 y  x  5
2x  y  3

x  4y  6
 x  7 y  5

3x  12y  3
SET A
2 4
8 10
14 16
Set B
6
12
18
3
9
15