If you could show how each steps done that would be helpful! Thank you. ### Problem 4: Probability in Northern Virginia Lawn Services#### Scenario:- 60% of homeowners in Northern Virginia have a weekly lawn service.- Of those with a lawn service, 55% have a sprinkler system.- Of those without a lawn service, 30% have a sprinkler system.**Note:** Express each answer in terms of the probability notation (e.g., P(A|B)).#### Tasks:a. **Draw a Tree Diagram** Model the problem using a tree diagram to represent the sequential probabilities of having a lawn service and sprinkler system.b. **Probability of Sprinkler System** - **Task:** Calculate the probability that a randomly selected home has a sprinkler system. - **Notation:** Use the law of total probability to find P(Sprinkler).c. **Probability of Lawn Service Given Sprinkler System** - **Task:** Determine the probability that a randomly selected home with a sprinkler system also has a lawn service. - **Notation:** Calculate P(Lawn Service | Sprinkler).d. **Probability of Sprinkler System Given Lawn Service** - **Task:** Find the probability that a randomly selected home with a lawn service has a sprinkler system. - **Notation:** Calculate P(Sprinkler | Lawn Service).e. **Probability of Having a Lawn Service** - **Task:** Determine the probability that a randomly selected home has a lawn service. - **Notation:** P(Lawn Service).f. **Probability of Sprinkler System Without Lawn Service** - **Task:** Calculate the probability that a randomly selected home that does not have a lawn service has a sprinkler system. - **Notation:** P(Sprinkler | No Lawn Service).

Name: If you could show how each steps done that would be helpful! Thank you
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Description: If you could show how each steps done that would be helpful! Thank you. ### Problem 4: Probability in Northern Virginia Lawn Services#### Scenario:- 60% of homeowners in Northern Virginia have a weekly lawn service.- Of those with a lawn service, 55%

Note: Thank you for the question. Since multiple subparts are posted, according to our policy, we…

Math

Probability

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?

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?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter6: Ratio, Proportion, And Probability

Section6.7: Probability And Odds

Problem 1C

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If you could show how each steps done that would be helpful! Thank you.

### Problem 4: Probability in Northern Virginia Lawn Services

#### Scenario:
- 60% of homeowners in Northern Virginia have a weekly lawn service.
- Of those with a lawn service, 55% have a sprinkler system.
- Of those without a lawn service, 30% have a sprinkler system.

**Note:** Express each answer in terms of the probability notation (e.g., P(A|B)).

#### Tasks:
a. **Draw a Tree Diagram**
Model the problem using a tree diagram to represent the sequential probabilities of having a lawn service and sprinkler system.

b. **Probability of Sprinkler System**
- **Task:** Calculate the probability that a randomly selected home has a sprinkler system.
- **Notation:** Use the law of total probability to find P(Sprinkler).

c. **Probability of Lawn Service Given Sprinkler System**
- **Task:** Determine the probability that a randomly selected home with a sprinkler system also has a lawn service.
- **Notation:** Calculate P(Lawn Service | Sprinkler).

d. **Probability of Sprinkler System Given Lawn Service**
- **Task:** Find the probability that a randomly selected home with a lawn service has a sprinkler system.
- **Notation:** Calculate P(Sprinkler | Lawn Service).

e. **Probability of Having a Lawn Service**
- **Task:** Determine the probability that a randomly selected home has a lawn service.
- **Notation:** P(Lawn Service).

f. **Probability of Sprinkler System Without Lawn Service**
- **Task:** Calculate the probability that a randomly selected home that does not have a lawn service has a sprinkler system.
- **Notation:** P(Sprinkler | No Lawn Service).

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