# 13.7 Probability  (Page 7/18)

 Page 7 / 18

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?

given 4cot thither +3=0and 0°<thither <180° use a sketch to determine the value of the following a)cos thither
what are you up to?
nothing up todat yet
Miranda
hi
jai
hello
jai
Miranda Drice
jai
aap konsi country se ho
jai
which language is that
Miranda
I am living in india
jai
good
Miranda
what is the formula for calculating algebraic
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
Miranda
state and prove Cayley hamilton therom
hello
Propessor
hi
Miranda
the Cayley hamilton Theorem state if A is a square matrix and if f(x) is its characterics polynomial then f(x)=0 in another ways evey square matrix is a root of its chatacteristics polynomial.
Miranda
hi
jai
hi Miranda
jai
thanks
Propessor
welcome
jai
What is algebra
algebra is a branch of the mathematics to calculate expressions follow.
Miranda
Miranda Drice would you mind teaching me mathematics? I think you are really good at math. I'm not good at it. In fact I hate it. 😅😅😅
Jeffrey
lolll who told you I'm good at it
Miranda
something seems to wispher me to my ear that u are good at it. lol
Jeffrey
lolllll if you say so
Miranda
but seriously, Im really bad at math. And I hate it. But you see, I downloaded this app two months ago hoping to master it.
Jeffrey
which grade are you in though
Miranda
oh woww I understand
Miranda
Jeffrey
Jeffrey
Miranda
how come you finished in college and you don't like math though
Miranda
gotta practice, holmie
Steve
if you never use it you won't be able to appreciate it
Steve
I don't know why. But Im trying to like it.
Jeffrey
yes steve. you're right
Jeffrey
so you better
Miranda
what is the solution of the given equation?
which equation
Miranda
I dont know. lol
Jeffrey
Miranda
Jeffrey
answer and questions in exercise 11.2 sums
how do u calculate inequality of irrational number?
Alaba
give me an example
Chris
and I will walk you through it
Chris
cos (-z)= cos z .
cos(- z)=cos z
Mustafa
what is a algebra
(x+x)3=?
6x
Obed
what is the identity of 1-cos²5x equal to?
__john __05
Kishu
Hi
Abdel
hi
Ye
hi
Nokwanda
C'est comment
Abdel
Hi
Amanda
hello
SORIE
Hiiii
Chinni
hello
Ranjay
hi
ANSHU
hiiii
Chinni
h r u friends
Chinni
yes
Hassan
so is their any Genius in mathematics here let chat guys and get to know each other's
SORIE
I speak French
Abdel
okay no problem since we gather here and get to know each other
SORIE
hi im stupid at math and just wanna join here
Yaona
lol nahhh none of us here are stupid it's just that we have Fast, Medium, and slow learner bro but we all going to work things out together
SORIE
it's 12
what is the function of sine with respect of cosine , graphically
tangent bruh
Steve
cosx.cos2x.cos4x.cos8x
sinx sin2x is linearly dependent
what is a reciprocal
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
Shemmy
Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
Jeza
each term in a sequence below is five times the previous term what is the eighth term in the sequence
I don't understand how radicals works pls