<< Chapter < Page Chapter >> Page >

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

What is the percent chance of winning?

Got questions? Get instant answers now!

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 %

Got questions? Get instant answers now!

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.)

Got questions? Get instant answers now!

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 %

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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 %

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Evaluate 6 ! ( 5 3 ) ! 3 ! .

Got questions? Get instant answers now!

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

13 , 103 , 1003 , 10003

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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 .

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

a 1 = 20 ,   a n = a n 1 + 10

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

a n = 1 3 n + 13 24

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Geometric Sequences

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

r = 2

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!
Practice Key Terms 9

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask