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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

the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success Reply
a man walks up 200 meters along a straight road whose inclination is 30 degree.How high above the starting level is he?
Lhorren Reply
100 meters
Kuldeep
Find that number sum and product of all the divisors of 360
jancy Reply
answer
Ajith
exponential series
Naveen
what is subgroup
Purshotam Reply
Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
Macmillan Reply
e power cos hyperbolic (x+iy)
Vinay Reply
10y
Michael
tan hyperbolic inverse (x+iy)=alpha +i bita
Payal Reply
prove that cos(π/6-a)*cos(π/3+b)-sin(π/6-a)*sin(π/3+b)=sin(a-b)
Tejas Reply
why {2kπ} union {kπ}={kπ}?
Huy Reply
why is {2kπ} union {kπ}={kπ}? when k belong to integer
Huy
if 9 sin theta + 40 cos theta = 41,prove that:41 cos theta = 41
Trilochan Reply
what is complex numbers
Ayushi Reply
Please you teach
Dua
Yes
ahmed
Thank you
Dua
give me treganamentry question
Anshuman Reply
Solve 2cos x + 3sin x = 0.5
shobana 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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