1. Home
  2. Elementary statistics
  3. Probability topics
  4. Exercises

4.6 Exercises

<< Chapter < Page
  Elementary statistics     Page 1 / 2
Chapter >> Page >
This module provides a number of homework exercises related to Probability.

Suppose that you have 8 cards. 5 are green and 3 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 3 yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card.

  • G = card drawn is green
  • E = card drawn is even-numbered
  • List the sample space.
  • P(G) =
  • P(G|E) =
  • P(G AND E) =
  • P(G OR E) =
  • Are G and E mutually exclusive? Justify your answer numerically.
  • {G1, G2, G3, G4, G5, Y1, Y2, Y3}
  • 5 8
  • 2 3
  • 2 8 size 12{ { { size 8{2} } over { size 8{8} } } } {}
  • 6 8 size 12{ { { size 8{6} } over { size 8{8} } } } {}
  • No

Refer to the previous problem. Suppose that this time you randomly draw two cards, one at a time, and with replacement .

  • G 1 = first card is green
  • G 2 = second card is green
  • Draw a tree diagram of the situation.
  • P ( G 1  AND  G 2 ) = size 12{P \( G rSub { size 8{1} } " and "G rSub { size 8{2} } \) ={}} {}
  • P ( at least one green ) = size 12{P \( "at least one green" \) ={}} {}
  • P ( G 2 ∣ G 1 ) = size 12{P \( G rSub { size 8{2} } \lline G rSub { size 8{1} } \) ={}} {}
  • Are G 2 size 12{G rSub { size 8{2} } } {} and G 1 size 12{G rSub { size 8{1} } } {} independent events? Explain why or why not.

Refer to the previous problems. Suppose that this time you randomly draw two cards, one at a time, and without replacement .

  • G 1 = first card is green
  • G 2 = second card is green
  • Draw a tree diagram of the situation.
  • P( G 1  AND  G 2 ) =
  • P(at least one green) =
  • P( G 2 | G 1 ) =
  • Are G 2 and G 1 independent events? Explain why or why not.
  • ( 5 8 ) ( 4 7 ) size 12{ \( { { size 8{5} } over { size 8{8} } } \) \( { { size 8{4} } over { size 8{7} } } \) } {}
  • ( 5 8 ) ( 3 7 ) + ( 3 8 ) ( 5 7 ) + ( 5 8 ) ( 4 7 ) size 12{ \( { { size 8{5} } over { size 8{8} } } \) \( { { size 8{3} } over { size 8{7} } } \) + \( { { size 8{3} } over { size 8{8} } } \) \( { { size 8{5} } over { size 8{7} } } \) + \( { { size 8{5} } over { size 8{8} } } \) \( { { size 8{4} } over { size 8{7} } } \) } {}
  • 4 7 size 12{ { { size 8{4} } over { size 8{7} } } } {}
  • No

Roll two fair dice. Each die has 6 faces.

  • List the sample space.
  • Let A be the event that either a 3 or 4 is rolled first, followed by an even number. Find P(A) .
  • Let B be the event that the sum of the two rolls is at most 7. Find P(B) .
  • In words, explain what “ P(A|B) ” represents. Find P(A|B) .
  • Are A and B mutually exclusive events? Explain your answer in 1 - 3 complete sentences, including numerical justification.
  • Are A and B independent events? Explain your answer in 1 - 3 complete sentences, including numerical justification.

A special deck of cards has 10 cards. Four are green, three are blue, and three are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin.

  • List the sample space.
  • Let A be the event that a blue card is picked first, followed by landing a head on the coin toss. Find P(A) .
  • Let B be the event that a red or green is picked, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? Explain your answer in 1 - 3 complete sentences, including numerical justification.
  • Let C be the event that a red or blue is picked, followed by landing a head on the coin toss. Are the events A and C mutually exclusive? Explain your answer in 1 - 3 complete sentences, including numerical justification.
  • { GH , GT , BH , BT , RH , RT } size 12{ lbrace ital "GH", ital "GT", ital "BH", ital "BT", ital "RH", ital "RT" rbrace } {}
  • 3 20 size 12{ { { size 8{3} } over { size 8{"20"} } } } {}
  • Yes
  • No

An experiment consists of first rolling a die and then tossing a coin:

  • List the sample space.
  • Let A be the event that either a 3 or 4 is rolled first, followed by landing a head on the coin toss. Find P(A) .
  • Let B be the event that a number less than 2 is rolled, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? Explain your answer in 1 - 3 complete sentences, including numerical justification.

An experiment consists of tossing a nickel, a dime and a quarter. Of interest is the side the coin lands on.

  • List the sample space.
  • Let A be the event that there are at least two tails. Find P(A) .
  • Let B be the event that the first and second tosses land on heads. Are the events A and B mutually exclusive? Explain your answer in 1 - 3 complete sentences, including justification.
  • { ( HHH ) , ( HHT ) , ( HTH ) , ( HTT ) , ( THH ) , ( THT ) , ( TTH ) , ( TTT ) } size 12{ lbrace \( ital "HHH" \) , \( ital "HHT" \) , \( ital "HTH" \) , \( ital "HTT" \) , \( ital "THH" \) , \( ital "THT" \) , \( ital "TTH" \) , \( ital "TTT" \) rbrace } {}
  • 4 8 size 12{ { { size 8{4} } over { size 8{8} } } } {}
  • Yes

Questions & Answers

differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
what is labour ?
Lambiv
how will I do?
Venny Reply
how is the graph works?I don't fully understand
Rezat Reply
information
Eliyee
devaluation
Eliyee
t
WARKISA
hi guys good evening to all
Lambiv
multiple choice question
Aster Reply
appreciation
Eliyee
explain perfect market
Lindiwe Reply
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
yes,thank you
Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Lilia Reply
what is the difference between economic growth and development
Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
Abdisa Reply
any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
Feyisa Reply
Answer
Feyisa
c
Jabir
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
Gsbwnw Reply
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
types of unemployment
Yomi Reply
What is the difference between perfect competition and monopolistic competition?
Mohammed
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>

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, Elementary statistics. OpenStax CNX. Dec 30, 2013 Download for free at http://cnx.org/content/col10966/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

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

Ask