# 3.5 Tree and venn diagrams  (Page 2/10)

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## Try it

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.

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 ) =
2. P ( N | F ) = $\frac{40}{51}$
3. P (at most one face card) = = $\frac{2,520}{2,652}$
4. P (at least one face card) = = $\frac{\text{1,092}}{\text{2,652}}$

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.

1. What is the probability that both kittens are tabby?
a. $\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)$ b. $\left(\frac{4}{9}\right)\left(\frac{4}{9}\right)$ c. $\left(\frac{4}{9}\right)\left(\frac{3}{8}\right)$ d. $\left(\frac{4}{9}\right)\left(\frac{5}{9}\right)$
2. What is the probability that one kitten of each coloring is selected?
a. $\left(\frac{4}{9}\right)\left(\frac{5}{9}\right)$ b. $\left(\frac{4}{9}\right)\left(\frac{5}{8}\right)$ c. $\left(\frac{4}{9}\right)\left(\frac{5}{9}\right)+\left(\frac{5}{9}\right)\left(\frac{4}{9}\right)$ d. $\left(\frac{4}{9}\right)\left(\frac{5}{8}\right)+\left(\frac{5}{9}\right)\left(\frac{4}{8}\right)$
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. $\frac{4}{8}$ , d. $\frac{32}{72}$

## Try it

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?

$\left(\frac{4}{7}\right)\left(\frac{3}{6}\right)$ + $\left(\frac{3}{7}\right)\left(\frac{4}{6}\right)$

## 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:

## Try it

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.

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:

## Try it

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.

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.

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.
• 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

What is the variances of 568
friend
what variance would have a single value..?
friend
variance happened only in a group of values..
friend
if we have a group of values...1st we find its average..ie..'mean'..then we calculate each value's difeerence from the mean..then we will square each 'difference value'.then we devide total of sqared value by n or n-1..that is what variance...
friend
What is the variances of 258
66,564
Mampy
what is the sample size if the degree of freedom is 25?
26..
friend
25
Tariku
27
Tariku
degrees of freedom may differ with respect to distribution...so tell which distribution you have selected...?
friend
my distribution is 27
Tariku
how to understand statistics
you are working for a bank.The bank manager wants to know the mean waiting time for all customers who visit this bank. she has asked you to estimate this mean by taking a sample . Briefly explain how you will conduct this study. assume the data set on waiting times for 10 customers who visit a bank. Then estimate the population mean. choose your own confidence level.
what marriage for 10 years
fit a least square model of y on x ? what is the regression coefficient ? x : 2 3 6 8 9 10 y : 5 6 7 10 8 11
how can we find the expectation of any function of X?
Jennifer
I've been using this app for some time now. I'm taking a stats class in college in spring and I still have no idea what's going on. I'm also 55 yrs old. Is there another app for people like me?
Tamala
Serious
Hamza
yes I am. it's been decades since I've been in school.
Tamala
who are u
zaheer
is there a private chat we can do
Tamala
hello how can I get PDF of solutions introduction mathematical statistics ( fourth education) who can help me
ahssal
can anyone help me
Halim
what is probability
simply probability means possibility.. definition:Probability is a measure of the likelihood of an event to occur.
laraib
fit a least square model of y on x ? what is the regression coefficient ? x : 2 3 6 8 9 10 y : 5 6 7 10 8 11
Nayab
classification of data by attributes is called
qualitative classification
talal
tell me details about measure of Dispersion
Halim
Following data provided Class Frequency less than 10 10-20 5 15 10-30 25 12 40 and above Which measure of central tendency would you compute and why?
a box contains a few red and a few blue balls.one ball is drawn randomly find the probability of getting a red ball if we know that there are 30 red and 40 blue balls in the box
3/7
RICH
Total=30+40=70 P(red balls) =30/70 Therefore the answer is 3/7
Anuforo
define transport statistical unit
describe each transport statistical unit
Dennis
explain uses of each transport statistical unit
Dennis
identify various transport statistical units with their example
Dennis
I didn't understand about Chi- square.
explain the concept of data analysis and data processing
mean=43+37+35+30+41+23+33+31+16/10 =310/10 =31
Anuforo
43+37+35+30+41+23+33+31+16 divided by 10 =310/10 =31
Anuforo
=310/10 =31
Anuforo