# 11.7 Probability  (Page 7/18)

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

$\text{\hspace{0.17em}}\frac{C\left(20,3\right)C\left(60,17\right)}{C\left(80,20\right)}\approx 12.49%\text{\hspace{0.17em}}$

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

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

$\text{\hspace{0.17em}}\frac{C\left(20,5\right)C\left(60,15\right)}{C\left(80,20\right)}\approx 23.33%\text{\hspace{0.17em}}$

What is the percent chance of winning?

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

$20.50+23.33-12.49=31.34%$

## 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.)

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.)

$\frac{C\left(40000000,1\right)C\left(277000000,4\right)}{C\left(317000000,5\right)}=36.78%$

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

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

$\frac{C\left(40000000,4\right)C\left(277000000,1\right)}{C\left(317000000,5\right)}=0.11%$

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?

## Sequences and Their Notation

Write the first four terms of the sequence defined by the recursive formula $\text{\hspace{0.17em}}{a}_{1}=2,\text{\hspace{0.17em}}{a}_{n}={a}_{n-1}+n.$

$2,4,7,11$

Evaluate $\text{\hspace{0.17em}}\frac{6!}{\left(5-3\right)!3!}.$

Write the first four terms of the sequence defined by the explicit formula $\text{\hspace{0.17em}}{a}_{n}={10}^{n}+3.$

$13,103,1003,10003$

Write the first four terms of the sequence defined by the explicit formula $\text{\hspace{0.17em}}{a}_{n}=\frac{n!}{n\left(n+1\right)}.$

## Arithmetic Sequences

Is the sequence $\text{\hspace{0.17em}}\frac{4}{7},\frac{47}{21},\frac{82}{21},\frac{39}{7},\text{\hspace{0.17em}}...$ arithmetic? If so, find the common difference.

The sequence is arithmetic. The common difference is $\text{\hspace{0.17em}}d=\frac{5}{3}.$

Is the sequence $\text{\hspace{0.17em}}2,4,8,16,\text{\hspace{0.17em}}...\text{\hspace{0.17em}}$ arithmetic? If so, find the common difference.

An arithmetic sequence has the first term $\text{\hspace{0.17em}}{a}_{1}=18\text{\hspace{0.17em}}$ and common difference $\text{\hspace{0.17em}}d=-8.\text{\hspace{0.17em}}$ What are the first five terms?

$18,10,2,-6,-14$

An arithmetic sequence has terms ${a}_{3}=11.7$ and ${a}_{8}=-14.6.$ What is the first term?

Write a recursive formula for the arithmetic sequence $-20\text{,}-10,0\text{,}10\text{,…}$

Write a recursive formula for the arithmetic sequence and then find the 31 st term.

Write an explicit formula for the arithmetic sequence

${a}_{n}=\frac{1}{3}n+\frac{13}{24}$

How many terms are in the finite arithmetic sequence $\text{\hspace{0.17em}}12,20,28,\dots ,172?$

## Geometric Sequences

Find the common ratio for the geometric sequence

$r=2$

Is the sequence geometric? If so find the common ratio. If not, explain why.

A geometric sequence has terms $\text{\hspace{0.17em}}{a}_{7}=16\text{,}384\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}{a}_{9}=262\text{,}144\text{\hspace{0.17em}.}$ What are the first five terms?

A geometric sequence has the first term $\text{\hspace{0.17em}}{a}_{1}\text{=}-3\text{\hspace{0.17em}}$ and common ratio $\text{\hspace{0.17em}}r=\frac{1}{2}.\text{\hspace{0.17em}}$ What is the 8 th term?

what is set?
a colony of bacteria is growing exponentially doubling in size every 100 minutes. how much minutes will it take for the colony of bacteria to triple in size
I got 300 minutes. is it right?
Patience
no. should be about 150 minutes.
Jason
It should be 158.5 minutes.
Mr
ok, thanks
Patience
100•3=300 300=50•2^x 6=2^x x=log_2(6) =2.5849625 so, 300=50•2^2.5849625 and, so, the # of bacteria will double every (100•2.5849625) = 258.49625 minutes
Thomas
what is the importance knowing the graph of circular functions?
can get some help basic precalculus
What do you need help with?
Andrew
how to convert general to standard form with not perfect trinomial
can get some help inverse function
ismail
Rectangle coordinate
how to find for x
it depends on the equation
Robert
yeah, it does. why do we attempt to gain all of them one side or the other?
Melissa
whats a domain
The domain of a function is the set of all input on which the function is defined. For example all real numbers are the Domain of any Polynomial function.
Spiro
Spiro; thanks for putting it out there like that, 😁
Melissa
foci (–7,–17) and (–7,17), the absolute value of the differenceof the distances of any point from the foci is 24.
difference between calculus and pre calculus?
give me an example of a problem so that I can practice answering
x³+y³+z³=42
Robert
dont forget the cube in each variable ;)
Robert
of she solves that, well ... then she has a lot of computational force under her command ....
Walter
what is a function?
I want to learn about the law of exponent
explain this
what is functions?
A mathematical relation such that every input has only one out.
Spiro
yes..it is a relationo of orders pairs of sets one or more input that leads to a exactly one output.
Mubita
Is a rule that assigns to each element X in a set A exactly one element, called F(x), in a set B.
RichieRich