60% of homeowners in Northern Virginia have a weekly lawn service. Those homes with a lawn service, 55% have a sprinkler system. For those without a lawn service, 30% have a sprinkler system. (Note: you do NOT need to simplify these answers. However, you MUST express each in terms of the events/probability notation - e.g., P(A|B) =...) a. Draw a tree diagram to model the problem b. What is the probability that a randomly selected home has a sprinkler system? c. What is the probability that a randomly selected home with a sprinkler system has a lawn service? d. What is the probability that a randomly selected home with a lawn service has a sprinkler system? e. What is the probability that a randomly selected home has a lawn service? f. What is the probability that a randomly selected home that does not have a lawn service has a sprinkler system?

Question
How to do this question?
60% of homeowners in Northern Virginia have a weekly lawn service. Those homes
with a lawn service, 55% have a sprinkler system. For those without a lawn service,
30% have a sprinkler system. (Note: you do NOT need to simplify these answers.
However, you MUST express each in terms of the events/probability notation - e.g.,
P(A|B) =...)
a. Draw a tree diagram to model the problem
b. What is the probability that a randomly selected home has a sprinkler
system?
c. What is the probability that a randomly selected home with a sprinkler
system has a lawn service?
d. What is the probability that a randomly selected home with a lawn service
has a sprinkler system?
e. What is the probability that a randomly selected home has a lawn service?
f. What is the probability that a randomly selected home that does not have
a lawn service has a sprinkler system?
Expand
Transcribed Image Text

60% of homeowners in Northern Virginia have a weekly lawn service. Those homes with a lawn service, 55% have a sprinkler system. For those without a lawn service, 30% have a sprinkler system. (Note: you do NOT need to simplify these answers. However, you MUST express each in terms of the events/probability notation - e.g., P(A|B) =...) a. Draw a tree diagram to model the problem b. What is the probability that a randomly selected home has a sprinkler system? c. What is the probability that a randomly selected home with a sprinkler system has a lawn service? d. What is the probability that a randomly selected home with a lawn service has a sprinkler system? e. What is the probability that a randomly selected home has a lawn service? f. What is the probability that a randomly selected home that does not have a lawn service has a sprinkler system?

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Probability

Venn Diagrams & Tree Diagrams

Conditional Probability

Related Probability Q&A

Find answers to questions asked by students like you.

Q: The fotlowing sample data represents the age of 30 lottery winners. 24 26 27 32 39 40 43 44 46 47 49...

A: the lowest value = 24 and the highest value = 84 so the range= R= 84 - 24= 60  So using the formula ...

Q: A researcher for the EPA mneasured the amount of arsenic in the water near a sewag treatment plant. ...

A: To find the number of measurements of less than 60 ppb we have to add all the frequencies below 60. ...

Q: please answer the question in the image.thank you

A: Click to see the answer

Q: 4.5-7 a and b only

A: Click to see the answer

Q: Scott wants to find a 95% confidence interval for the average GPA for Allegany College of Maryland s...

A: Click to see the answer

Q: Given: If X, then Y. If Y, then Z. Y is true. So: a) x is unknown, z is unknown b) x is unknown, z i...

A: GIVEN DATA : If X, then Y.                          If Y then Z. So, Y is true According to the give...

Q: A trainer is teaching a dolphin to do tricks. The probability that the dolphin successfullyperforms ...

A: Click to see the answer

Q: The cost of textbooks is normally distributed with a mean of $222. You do not know the population st...

A: Click to see the answer

Q: ) The mean time for an Auto repair shop to change the oil in a car is ? = 16.4 minutes with a standa...

A: 1) The probability that the mean time it takes for sixteen randomly selected oil change jobs at most...

Q: The mean gas mileage for a hybrid car is 57 miles per gallon. Suppose that the gasoline mileage is a...

A: Click to see the answer

Q: In a survery of men, the heights in the 20-29 age group were normally distributed, with a mean of in...

A: The random variable X is defined as the heights in the 20-29 age group which follows normal distribu...

Q: 3. The amount of calories in a slice of cheese pizza follows a Normal Distribution with a mean of264...

A: Click to see the answer

Q: find the area under the standard normal curve to the left of z=1.5

A: Area under the curve is the probability that continuous random variable lies in a given range.  

Q: There are four numbers in a data set. They are 5, 3, 7, and 11. a) What is the ∑∑ x2x2    b) What is...

A: Number of samples (n) = 4   X X2   5 25   3 9   7 49   11 121 Total

Q: 

A: Confidence interval are of utmost importance in statistics . It forms an integral part of hypothesis...

Q: Roulette with 44 slots. One with 0 another with 00 and umbers 1 to 42. You are placing a bet that th...

A: Total number of even numbers in 1 to 42 is = 422=21 0 and 00 are neither even nor odd.    So the num...

Q: A product has an average impurity of 0.735 g. A new product was manufactured for which it was obtain...

A: Given information: μ=0.735 x=0.710, s = 0.0504 Use the excel formula, "=T.INV.2T(0.05,19)" for deter...

Q: Make a list of the amounts of money one can have that cannot be reduced to a smaller number ofcoins....

A: In Glosia, currency consists of florins (f) , ecus (e) and  ducats (d). In Glosian money, f=2e, e=2d...

Q: There are five numbers in a data set. They are 1, 2, 18, 19 and x, where x is one of the largest two...

A: GIVEN DATA : The Five numbers in the data  set are : 1, 2, 18, 19, x                          Mean o...

Q: Cristiano walks to his friend’s house that is 9.3 miles away.   He stops for a snack when he is  2/...

A: Given that the total distance is 9.3 miles.  He stops after he walked 23 of the way.   

Q: Question1:-If 6 seats are empty in a train box and two man entered in this coach than they seated ho...

A: Hi there! Thanks for the questions, since there are multiple questions we have solved the first ques...

Q: part A

A: Refer to Standard normal table/Z-table to find the probability of z=0.33 and z=-0.33 to the left of ...

Q: Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the am...

A: Let "X" be the amount of beer poured by this filling machine in ounce.

Q: please answer the question in the image.thank you

A: Given Information: X is normally distributed with mean μ=10 and standard deviation σ=2 (a) To calcul...

Q: Assume that there is a 10% rate of disk failure in a year  A) if all your computer data is stored on...

A: P[a disk failure]=0.1,  (A) P[at least one working drive out of two]=1-P[none are working out of two...

Q: Rework problem 25 from section 3.2 of your text, involving choosing freshmen, sophomores, and junior...

A: Click to see the answer

Q: Suppose that 35% of all voters prefer Candidate A.If 7 people are chosen at random for a poll, what ...

A: Probability that voters prefer Candidate A = 35% = 0.35 Sample size, n = 7

Q: For data that is not normally distributed we can't use z-scores. However, there is an equation that ...

A: a) We have to find the minimum percentage of scores that fall within 3.3 standard deviations on both...

Q: The median is closest to:

A: The discount rate set by bank for past 6 quarters are: Quarter Discount Rate 1 10.0% ...

Q: Suppose a county’s recent health report gives a pet allergy prevalence of 0.23 for kids. There is a ...

A: Given: Probability of pet allergy prevalence, P(A)=0.23 kids Probability of no pet allergy prevalenc...

Q: Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and Ped...

A: Click to see the answer

Q: The red blood cell counts​ (in millions of cells per​ microliter) for a population of adult males ca...

A: Let us denote: X= The red blood cell count So, X follows a normal distribution with mean= 5.3 and st...

Q: Rework problem 24 from section 3.2 of your text, involving the subcommittee. For this problem, assum...

A: Given data, Number of men = 7 Number of women = 6 Total number of members = 7 + 6= 13

Q: Let px (x) be the pmf of a random variable X. Find the cdf F(z) of X and its graph along with that o...

A: a). Find the cdf F(x) of X and sketch the graph: The probability mass function is given below: X...

Q: You may need to use the appropriate appendix table or technology to answer this question. In a large...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: When purchasing bulk orders of batteries a toy manufacturer uses this acceptance sampling plan.  Ran...

A: Click to see the answer

Q: Alice and Bob are talking over a really slow telephone connection and want to avoid talking over eac...

A: Given, Each person makes 8 cards numbered 0, 1, 2, 3, 4, 5, 6, 7, shuffles them and picks one at ran...

Q: The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a stand...

A: The z-score corresponding to 71 inch tall American women is, Thus,  the percentage of women that ar...

Q: Environment-friendly agricultural practice includes the application of pesticides when it is really ...

A: Introduction: Denote X as the number of pest emergences in two weeks, which occurs at the rate of 1 ...

Q: According to TMUSS Quarterly (Totally Made-Up Sports Statistics) April 2017, the probability that th...

A: Given data:   The given probability that the Tampa Bay Buccaneers defend three or more sacks in a ga...

Q: 3-The results of CNN’s 2012 presidential election poll are given. Use the following table to answer ...

A: The results of CNN’s 2012 presidential election poll are given are tabulated below: a) The probabil...

Q: Consider a random 3 digit number from 000 to 999 (1000 in total). What is the probability of getting...

A: Given data:   A three-digit number from 000 to 999.   The total three-digit number that can be forme...

Q: Company XYZ know that replacement times for the portable MP3 players it produces are normally distri...

A: Let us assume that X=replacement times for the portable MP3 players Given that X follows a normal di...

Q: When we find conditional probabilities, do we need to check to see if they are mutually exclusive or...

A: Yes we need to check to see if they are mutually exclusive or if they are independent.    If A and B...

Q: Suppose you have 3 red marbles, 2 blue marbles, and 4 yellow marbles in a bag.  What is the sample s...

A: Given that there are 3 red marbles, 2 blue marbles, and 4 yellow marbles in a bag. I will pick 2 mar...

Q: A landscape gardener employs several students to help him with his work. One morning they come to wo...

A: Total number of gloves in the box = Number of left handed gloves + Number of right handed gloves    ...