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What is the percent chance that a player selects exactly 3 winning numbers?

C ( 20 , 3 ) C ( 60 , 17 ) C ( 80 , 20 ) 12.49 %

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What is the percent chance that a player selects exactly 4 winning numbers?

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What is the percent chance that a player selects all 5 winning numbers?

C ( 20 , 5 ) C ( 60 , 15 ) C ( 80 , 20 ) 23.33 %

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What is the percent chance of winning?

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How much less is a player’s chance of selecting 3 winning numbers than the chance of selecting either 4 or 5 winning numbers?

20.50 + 23.33 12.49 = 31.34 %

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Real-world applications

Use this data for the exercises that follow: In 2013, there were roughly 317 million citizens in the United States, and about 40 million were elderly (aged 65 and over). United States Census Bureau. http://www.census.gov

If you meet a U.S. citizen, what is the percent chance that the person is elderly? (Round to the nearest tenth of a percent.)

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If you meet five U.S. citizens, what is the percent chance that exactly one is elderly? (Round to the nearest tenth of a percent.)

C ( 40000000 , 1 ) C ( 277000000 , 4 ) C ( 317000000 , 5 ) = 36.78 %

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If you meet five U.S. citizens, what is the percent chance that three are elderly? (Round to the nearest tenth of a percent.)

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If you meet five U.S. citizens, what is the percent chance that four are elderly? (Round to the nearest thousandth of a percent.)

C ( 40000000 , 4 ) C ( 277000000 , 1 ) C ( 317000000 , 5 ) = 0.11 %

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It is predicted that by 2030, one in five U.S. citizens will be elderly. How much greater will the chances of meeting an elderly person be at that time? What policy changes do you foresee if these statistics hold true?

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Chapter review exercises

Sequences and Their Notation

Write the first four terms of the sequence defined by the recursive formula a 1 = 2 , a n = a n 1 + n .

2 , 4 , 7 , 11

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Evaluate 6 ! ( 5 3 ) ! 3 ! .

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Write the first four terms of the sequence defined by the explicit formula a n = 10 n + 3.

13 , 103 , 1003 , 10003

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Write the first four terms of the sequence defined by the explicit formula a n = n ! n ( n + 1 ) .

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Arithmetic Sequences

Is the sequence 4 7 , 47 21 , 82 21 , 39 7 , ... arithmetic? If so, find the common difference.

The sequence is arithmetic. The common difference is d = 5 3 .

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Is the sequence 2 , 4 , 8 , 16 , ... arithmetic? If so, find the common difference.

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An arithmetic sequence has the first term a 1 = 18 and common difference d = 8. What are the first five terms?

18 , 10 , 2 , 6 , 14

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An arithmetic sequence has terms a 3 = 11.7 and a 8 = 14.6. What is the first term?

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Write a recursive formula for the arithmetic sequence 20 , 10 , 0 , 10 ,…

a 1 = 20 ,   a n = a n 1 + 10

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Write a recursive formula for the arithmetic sequence 0 ,   1 2 ,   1 ,   3 2 , , and then find the 31 st term.

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Write an explicit formula for the arithmetic sequence 7 8 ,   29 24 ,   37 24 ,   15 8 ,

a n = 1 3 n + 13 24

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How many terms are in the finite arithmetic sequence 12 , 20 , 28 , , 172 ?

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Geometric Sequences

Find the common ratio for the geometric sequence 2.5 ,   5 ,   10 ,   20 ,

r = 2

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Is the sequence 4 ,   16 ,   28 ,   40 , geometric? If so find the common ratio. If not, explain why.

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A geometric sequence has terms a 7 = 16 , 384 and a 9 = 262 , 144  . What are the first five terms?

4 ,   16 ,   64 ,   256 ,   1024

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A geometric sequence has the first term a 1 = 3 and common ratio r = 1 2 . What is the 8 th term?

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Questions & Answers

if tan alpha + beta is equal to sin x + Y then prove that X square + Y square - 2 I got hyperbole 2 Beta + 1 is equal to zero
Rahul Reply
sin^4+sin^2=1, prove that tan^2-tan^4+1=0
SAYANTANI Reply
what is the formula used for this question? "Jamal wants to save $54,000 for a down payment on a home. How much will he need to invest in an account with 8.2% APR, compounding daily, in order to reach his goal in 5 years?"
Kuz Reply
i don't need help solving it I just need a memory jogger please.
Kuz
A = P(1 + r/n) ^rt
Dale
how to solve an expression when equal to zero
Mintah Reply
its a very simple
Kavita
gave your expression then i solve
Kavita
Hy guys, I have a problem when it comes on solving equations and expressions, can you help me 😭😭
Thuli
Tomorrow its an revision on factorising and Simplifying...
Thuli
ok sent the quiz
kurash
send
Kavita
Hi
Masum
What is the value of log-1
Masum
the value of log1=0
Kavita
Log(-1)
Masum
What is the value of i^i
Masum
log -1 is 1.36
kurash
No
Masum
no I m right
Kavita
No sister.
Masum
no I m right
Kavita
tan20°×tan30°×tan45°×tan50°×tan60°×tan70°
Joju Reply
jaldi batao
Joju
Find the value of x between 0degree and 360 degree which satisfy the equation 3sinx =tanx
musah Reply
what is sine?
tae Reply
what is the standard form of 1
Sanjana Reply
1×10^0
Akugry
Evalute exponential functions
Sujata Reply
30
Shani
The sides of a triangle are three consecutive natural number numbers and it's largest angle is twice the smallest one. determine the sides of a triangle
Jaya Reply
Will be with you shortly
Inkoom
3, 4, 5 principle from geo? sounds like a 90 and 2 45's to me that my answer
Neese
answer is 2, 3, 4
Gaurav
prove that [a+b, b+c, c+a]= 2[a b c]
Ashutosh Reply
can't prove
Akugry
i can prove [a+b+b+c+c+a]=2[a+b+c]
this is simple
Akugry
hi
Stormzy
x exposant 4 + 4 x exposant 3 + 8 exposant 2 + 4 x + 1 = 0
HERVE Reply
x exposent4+4x exposent3+8x exposent2+4x+1=0
HERVE
How can I solve for a domain and a codomains in a given function?
Oliver Reply
ranges
EDWIN
Thank you I mean range sir.
Oliver
proof for set theory
Kwesi Reply
don't you know?
Inkoom
find to nearest one decimal place of centimeter the length of an arc of circle of radius length 12.5cm and subtending of centeral angle 1.6rad
Martina Reply
Practice Key Terms 9

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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