Download Notes - Algebra II

1-115 Counting & Probability
Name: ________________________________________
Probability Notes:
Objectives: Be able to write out a sample space. Be able to calculate the probability of an event. Be
able to count a sequence of numbers.
Definitions:
Sample Space: ____________________________________________________________________
Event: __________________________________________________________________________
P  A 
1. Suppose we roll a die.
a) Write out the sample space of rolling a die.
b) What is the probability of the following events?
i.
A  Roll a 2 
ii.
B  Roll a 2 or a 3 
iii.
C  Roll an even number 
iv.
D  Roll a number less than or equal to 6
v.
E  Roll a 0 
2. Suppose we flip three coins.
a) Write out the sample space of tossing three coins.
b) What’s the probability of the following events?
i.
A  Get no heads 
ii.
B  Get 2 heads 
iii.
A  Get 2 heads or 2 Tails 

Counting Notes
1. How many numbers are in the list?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23
2. How many numbers are in the list?
7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32
3. How many numbers are there between 8 and 42 inclusive?
4. Given two positive numbers a and b, with a  b , find a formula for how many numbers there are
between a and b inclusive.
5. How many multiples of 3 are between 62 and 215?
6. How many multiples of 10 are between 9 and 101?
7. How many multiples of 10 are between 11 and 103?
8. How many 4 digit numbers are perfect cubes?
Exercises:
1. How many numbers are in the list 36, 37, 38, …, 92, 93?
2. How many numbers are in the list 4, 6, 8, …, 128, 130?
3. How many numbers are in the list -33, -28, -23, …, 52, 57?
4. How many numbers are in the list 147, 144, 141, …, 42, 39?
5. How many numbers are in the list 3 23 , 4 13 , 5, 5 32 , ..., 26 13 , 27?
6. How many positive multiples of 7 are less than 150?
7. How many perfect squares are between 50 and 250?
8. How many odd perfect squares are between 5 and 211?
9. How many sets of four consecutive positive integers are there such that the product of the four
integers is less that 100,000?
10. A couple plans to have two children.
a) List the different outcomes according to gender of each child (sample space).
b) Find the probability of getting two girls:___________________________________
c) Find the probability of getting exactly one child of each gender:______________________
3. A couple plans to have four children.
a) List all the outcomes according to gender of each child (sample space).
b) Find the probability of getting all girls:__________________________
c) Find the probability of getting at least one child of each gender:_____________________
d) Find the probability of getting exactly two children of each gender:____________________
4. On a quiz consisting of three true/false questions, an unprepared student must guess at each one.
The guesses are random.
a) Write out the sample space for the possible answers. One possibility is TTT.
b) What is the probability of answering all three questions correctly? _____________________
c) What is the probability of guessing incorrectly for all questions?_______________________
d) What is the probability of correctly guessing two questions?__________________________