<< Chapter < Page 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

What are types of cell
Nansoh Reply
how can I get this book
Gatyin Reply
what is lump
Chineye Reply
what is cell
Maluak Reply
what is biology
Maluak
what's cornea?
Majak Reply
what are cell
Achol
Explain the following terms . (1) Abiotic factors in an ecosystem
Nomai Reply
Abiotic factors are non living components of ecosystem.These include physical and chemical elements like temperature,light,water,soil,air quality and oxygen etc
Qasim
what is biology
daniel Reply
what is diffusion
Emmanuel Reply
passive process of transport of low-molecular weight material according to its concentration gradient
AI-Robot
what is production?
Catherine
Pathogens and diseases
how did the oxygen help a human being
Achol Reply
how did the nutrition help the plants
Achol Reply
Biology is a branch of Natural science which deals/About living Organism.
Ahmedin Reply
what is phylogeny
Odigie Reply
evolutionary history and relationship of an organism or group of organisms
AI-Robot
ok
Deng
what is biology
Hajah Reply
cell is the smallest unit of the humanity biologically
Abraham
ok
Achol
what is biology
Victoria Reply
what is biology
Abraham
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

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