1. Home
  2. Introductory statistics
  3. Probability topics
  4. Tree and venn diagrams

3.5 Tree and venn diagrams  (Page 4/10)

<< Chapter < Page
  Introductory statistics     Page 4 / 10
Chapter >> Page >

Chapter review

A tree diagram use branches to show the different outcomes of experiments and makes complex probability questions easy to visualize.

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. A Venn diagram is especially helpful for visualizing the OR event, the AND event, and the complement of an event and for understanding conditional probabilities.

The probability that a man develops some form of cancer in his lifetime is 0.4567. The probability that a man has at least one false positive test result (meaning the test comes back for cancer when the man does not have it) is 0.51. Let: C = a man develops cancer in his lifetime; P = man has at least one false positive. Construct a tree diagram of the situation.

This is a tree diagram with two branches. The first branch, labeled Cancer, shows two lines: 0.4567 C and 0.5433 C'. The second branch is labeled False Positive. From C, there are two lines: 0 P and 1 P'. From C', there are two lines: 0.51 P and 0.49 P'.
Got questions? Get instant answers now!

Bringing it together

Use the following information to answer the next two exercises. Suppose that you have eight cards. Five are green and three are yellow. The cards are well shuffled.

Suppose that you randomly draw two cards, one at a time, with replacement .
Let G 1 = first card is green
Let G 2 = second card is green

  1. Draw a tree diagram of the situation.
  2. Find P ( G 1 AND G 2 ).
  3. Find P (at least one green).
  4. Find P ( G 2 | G 1 ).
  5. Are G 2 and G 1 independent events? Explain why or why not.
  1. This is a tree diagram with branches showing probabilities of each draw. The first branch shows two lines: 5/8 Green and 3/8 Yellow. The second branch has a set of two lines (5/8 Green and 3/8 Yellow) for each line of the first branch.
  2. P ( GG ) = ( 5 8 ) ( 5 8 ) = 25 64
  3. P (at least one green) = P ( GG ) + P ( GY ) + P ( YG ) = 25 64 + 15 64 + 15 64 = 55 64
  4. P ( G | G ) = 5 8
  5. Yes, they are independent because the first card is placed back in the bag before the second card is drawn; the composition of cards in the bag remains the same from draw one to draw two.
Got questions? Get instant answers now!

Suppose that you randomly draw two cards, one at a time, without replacement .
G 1 = first card is green
G 2 = second card is green

  1. Draw a tree diagram of the situation.
  2. Find P ( G 1 AND G 2 ).
  3. Find P (at least one green).
  4. Find P ( G 2 | G 1 ).
  5. Are G 2 and G 1 independent events? Explain why or why not.
Got questions? Get instant answers now!

Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) that are female is 48.60. Of the females, 5.03% are age 19 and under; 81.36% are age 20–64; 13.61% are age 65 or over. Of the licensed U.S. male drivers, 5.04% are age 19 and under; 81.43% are age 20–64; 13.53% are age 65 or over.

Complete the following.

  1. Construct a table or a tree diagram of the situation.
  2. Find P (driver is female).
  3. Find P (driver is age 65 or over|driver is female).
  4. Find P (driver is age 65 or over AND female).
  5. In words, explain the difference between the probabilities in part c and part d.
  6. Find P (driver is age 65 or over).
  7. Are being age 65 or over and being female mutually exclusive events? How do you know?
  1. <20 20–64 >64 Totals
    Female 0.0244 0.3954 0.0661 0.486
    Male 0.0259 0.4186 0.0695 0.514
    Totals 0.0503 0.8140 0.1356 1
  2. P ( F ) = 0.486
  3. P (>64| F ) = 0.1361
  4. P (>64 and F ) = P ( F ) P (>64| F ) = (0.486)(0.1361) = 0.0661
  5. P (>64| F ) is the percentage of female drivers who are 65 or older and P (>64 and F ) is the percentage of drivers who are female and 65 or older.
  6. P (> 64 ) = P (>64 and F ) + P (>64 and M ) = 0.1356
  7. No, being female and 65 or older are not mutually exclusive because they can occur at the same time P(>64 and F ) = 0.0661.
Got questions? Get instant answers now!

Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice FlashCards 3 Key Terms 2

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications?

Ask