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In a standard deck, there are 52 cards. Twelve cards are face cards ( F ) and 40 cards are not face cards ( N ). Draw two cards, one at a time, without replacement. The tree diagram is labeled with all possible probabilities.

This is a tree diagram with branches showing frequencies of each draw. The first branch shows 2 lines: F 12/52 and N 40/52. The second branch has a set of 2 lines (F 11/52 and N 40/51) for each line of the first branch. Multiply along each line to find FF 121/2652, FN 480/2652, NF 480/2652, and NN 1560/2652.
  1. Find P ( FN OR NF ).
  2. Find P ( N | F ).
  3. Find P (at most one face card).
    Hint: "At most one face card" means zero or one face card.
  4. Find P (at least on face card).
    Hint: "At least one face card" means one or two face cards.
  1. P ( FN OR NF ) = 480 2,652  +  480 2,652  =  960 2,652  =  80 221
  2. P ( N | F ) = 40 51
  3. P (at most one face card) = (480  +  480  +  1,560) 2,652 = 2 , 520 2 , 652
  4. P (at least one face card) = (132 + 480 + 480) 2,652 = 1,092 2,652
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A litter of kittens available for adoption at the Humane Society has four tabby kittens and five black kittens. A family comes in and randomly selects two kittens (without replacement) for adoption.

This is a tree diagram with branches showing probabilities of kitten choices. The first branch shows two lines: T 4/9 and B 5/9. The second branch has a set of 2 lines for each first branch line. Below T 4/9 are T 3/8 and B 5/8. Below B 5/9 are T 4/8 and B 4/8. Multiply along each line to find probabilities of possible combinations.

  1. What is the probability that both kittens are tabby?
    a. ( 1 2 ) ( 1 2 ) b. ( 4 9 ) ( 4 9 ) c. ( 4 9 ) ( 3 8 ) d. ( 4 9 ) ( 5 9 )
  2. What is the probability that one kitten of each coloring is selected?
    a. ( 4 9 ) ( 5 9 ) b. ( 4 9 ) ( 5 8 ) c. ( 4 9 ) ( 5 9 ) + ( 5 9 ) ( 4 9 ) d. ( 4 9 ) ( 5 8 ) + ( 5 9 ) ( 4 8 )
  3. What is the probability that a tabby is chosen as the second kitten when a black kitten was chosen as the first?
  4. What is the probability of choosing two kittens of the same color?

a. c, b. d, c. 4 8 , d. 32 72

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Suppose there are four red balls and three yellow balls in a box. Three balls are drawn from the box without replacement. What is the probability that one ball of each coloring is selected?

( 4 7 ) ( 3 6 ) + ( 3 7 ) ( 4 6 )

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Venn diagram

A Venn diagram is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events.

Suppose an experiment has the outcomes 1, 2, 3, ... , 12 where each outcome has an equal chance of occurring. Let event A = {1, 2, 3, 4, 5, 6} and event B = {6, 7, 8, 9}. Then A AND B = {6} and A  OR  B = {1, 2, 3, 4, 5, 6, 7, 8, 9}. The Venn diagram is as follows:

A Venn diagram. An oval representing set A contains the values 1, 2, 3, 4, 5, and 6. An oval representing set B also contains the 6, along with 7, 8, and 9. The values 10, 11, and 12 are present but not contained in either set.
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Suppose an experiment has outcomes black, white, red, orange, yellow, green, blue, and purple, where each outcome has an equal chance of occurring. Let event C = {green, blue, purple} and event P = {red, yellow, blue}. Then C AND P = {blue} and C OR P = {green, blue, purple, red, yellow}. Draw a Venn diagram representing this situation.

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Flip two fair coins. Let A = tails on the first coin. Let B = tails on the second coin. Then A = { TT , TH } and B = { TT , HT }. Therefore, A AND B = { TT }. A OR B = { TH , TT , HT }.

The sample space when you flip two fair coins is X = { HH , HT , TH , TT }. The outcome HH is in NEITHER A NOR B . The Venn diagram is as follows:

This is a venn diagram. An oval representing set A contains Tails + Heads and Tails + Tails. An oval representing set B also contains Tails + Tails, along with Heads + Tails. The universe S contains Heads + Heads, but this value is not contained in either set A or B.
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Roll a fair, six-sided die. Let A = a prime number of dots is rolled. Let B = an odd number of dots is rolled. Then A = {2, 3, 5} and B = {1, 3, 5}. Therefore, A AND B = {3, 5}. A OR B = {1, 2, 3, 5}. The sample space for rolling a fair die is S = {1, 2, 3, 4, 5, 6}. Draw a Venn diagram representing this situation.

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Forty percent of the students at a local college belong to a club and 50% work part time. Five percent of the students work part time and belong to a club. Draw a Venn diagram showing the relationships. Let C = student belongs to a club and PT = student works part time.

This is a venn diagram with one set containing students in clubs and another set containing students working  part-time. Both sets share students who are members of clubs and also work part-time. The universe is labeled S.

If a student is selected at random, find

  • the probability that the student belongs to a club. P ( C ) = 0.40
  • the probability that the student works part time. P ( PT ) = 0.50
  • the probability that the student belongs to a club AND works part time. P ( C AND PT ) = 0.05
  • the probability that the student belongs to a club given that the student works part time. P ( C | P T )   =   P ( C  AND  P T ) P ( P T )   =   0.05 0.50   =   0.1
  • the probability that the student belongs to a club OR works part time. P ( C OR PT ) = P ( C ) + P ( PT ) - P ( C AND PT ) = 0.40 + 0.50 - 0.05 = 0.85
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Questions & Answers

Just a test from gplay
Lucy Reply
how come 5.67
Mano Reply
by dividing 11.37 on 2
saifuddin
by dividing 11.34 on 2
saifuddin
what is index number?
vinayak
What is the differences between quota an lottery system of sampling
EGBE
What are the are the characteristics that are critically expedients in selecting the sample size
EGBE
fit a binomial distribution for the following data and test the goodness of fit x: 0 1 2 3 4 5 6 f: 5 18 28 12 7 6 4
Mikki Reply
solution
Mano
solve the question please
Mano
can some please help solve so that we learn some
Simonsakala
It is a square chi
Nelson
But can't be a binomial because, the x numbers are 0 to 6, instead those would be "0" or "1" in a straight way
Nelson
You can do a chi-square test, but the assumption has to be a normal distribution, and the last f's number need to be "64"
Nelson
sorry the last f's numbers : "6 and 4" which are the observed values for 5 and 6 (expected values)
Nelson
hi
rajendra
can't understand basic of statistics ..
rajendra
Sorry I see my mistake, we have to calculate the expected values
Nelson
So we need this equation: P= (X=x)=(n to x) p^x(1-p)^n-x
Nelson
why it is not possible brother
ibrar
were n= 2 ( binomial) x= number of makes (0 to 6) and p= probability, could be 0.8.
Nelson
so after we calculate the expected values for each observed value (f) we do the chi-square. x^2=summatory(observed-expected)^2 / expected and compare with x^2 in table with 0.8
Nelson
tomorrow I'll post the answer, I'm so tired today, sorry for my mistake in the first messages.
Nelson
It is possible, sorry for my mistake
Nelson
two trader shared investment and buoght Cattle.Mr.Omer bought 255 cows & rented the farm for a period of 32 days. Mr. Ahmed grazed his Cattle for 25 days. Mr. Ahmed's cattle was 180 cows.Together they profited $ 7800. the rent of the farm is $ 3000 so divide the profit per gows/day for grazing day
Mohamed
how to start this book, who is reading thins first time
Nissar Reply
It is my first time reading this book
Qader
Good one
ihsan
from were did you get 2/50?m
Chico Reply
People living longer
Qader Reply
Why do you think that is?
Jazzy
because there is an increase in number of people with age more than 30.
Qader
Ok. And what do you think is the driving factor behind that hypothesis?
Jazzy
fewer birth and increase in # of years living or fewer dying
Qader
What about the improvement of technology and medicine?
Jazzy
hi,why the mean =sum(xi)/n but the variance =sum(xi-xbar)/ n-1 what is the difference between (n or n-1)
Soran Reply
This is hard to type, so I'll use "m" for "x bar", and a few other notations that I hope will be clear: Definition: sqrt(SUM[(x - m)^2] / (n-1)) where m = SUM[x] / n Desired formula: sqrt((SUM[x^2] - SUM[x]^2)/n / (n-1)) Now let's do what you started to do, and see if we can manipulate the definitio
Michael
what is the difference between (n ) and (n-1) in the mean and variance
Soran
Definition: sqrt(SUM[(x - m)^2] / (n-1)) where m = SUM[x] / n what is the difference between (n and n-1)
Soran
Hi, the diference is tha when we estimate parameters in a sample (not in the total population) we need to consider the degrees of liberty for the estimation.
Nelson
Hie guys, am analysing rainfall data for different stations and i got kurtosis values of 0.7 for one station and 0.4 for another, what can i say about this?
Kudakwashe
hi
ujjal
difference in degrees of freedom
vinayak
who introduced the statistics in england
Sunday Reply
what year is data first used
Sunday
Gottfried achievell is a professor at
Sunday Reply
hi
Soran
hello
mskinne4
hi
Raja
hello
Tshepo
freakin annoying chat. uninstalled
KickingtheDonksNuts
Hi
Sunday
hello
Inoxent
Hello rumiex
Abimbola
How is ur day going
Abimbola
Pls I hv a question 🙋 to ask
Abimbola
I want to ask, as a student who wants to study mechatronic engineering in the University. What are the necessary subject he or she needed, and after ur service were can or she work as a graduate
Abimbola
?
Abimbola
hello
Gh
Write a short note on skewness
Saran Reply
and on kurtosis too
Hiren
What is events
Manish Reply
IT occurs in probability
Peter
yes
Preeti
any experiment done
Preeti
who introduced statistics in england
Sunday
who is a strong man?
Desmond Reply
who never gives up
Preeti
Who eats lots of food 😂
abhinav
A man with great physical strength
Nucks
I still fetch confused about this statistics
Mustapha
hi
Samuel
hlw
Suman
hy
ibrar
One who withstand everything that was meant to break him.
Jazzy
"The stronger is not he who puts down his opponent on the ground but the stronger is he who controls himself in a pit of anger" (Bukhari Sharif)
saifuddin
still contemplating about analyzing statistical methods
solomon
Can you sir plz provide all the multiple choice questions related to Index numbers.?
Hiren Reply
about probabilty i have some questions and i want the solution
asad Reply
What is hypothesis?
Rosendo Reply
its a scientific guess
ted
A hypothesis in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon. In a scientific experiment or study, the hypothesis is a brief summation of the researcher's prediction of the study's findings.
Hamzah
Which may be supported or not by the outcome. Hypothesis testing is the core of the scientific method.
Hamzah
statistics means interpretation analysis and representation of numerical data
Ramzan
To check the statment or assumption about population parameter is xalled hypothesis
Ali
hypothesis is simply an assumption
Patrick

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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