SAT College

A landscaping company currently has an inventory of 8 fruit trees, 13 pine trees, and 14 maple trees. It plans to give 4 trees away at next
Saturday's lawn and garden show in the city park. The 4 winners can select which type of tree they want. Assume they select randomly.
a. What is the probability that all 4 winners will select the same type of tree?
b. What is the probability that 3 pine trees will be selected and the other tree will be a maple?
c. What is the probability that no fruit trees and 2 of each of the others will be selected?
a. The probability is
(Round to four decimal places as needed.)

Answers

Answer 1

The distribution of the trees in the landscape company is an illustration of probability

The probability that all 4 winners will select the same type of tree is 0.0341The probability that 3 pine trees will be selected and the other tree will be a maple is 0.0710The probability that no fruit trees and 2 of each of the others will be selected is 0.0904

a. The probability that all 4 winners will select the same type of tree?

The distribution of the trees are:

Fruit trees = 8Pine trees = 13Maple trees = 14

Total = 8 + 13 + 14

Total = 35

The probability is then calculated as:

P(Same type) = P(All fruit trees) + P(All pine trees) + P(All maple trees)

So, we have:

P(Same type) = (8/35 * 7/34 * 6/33 * 5/32) + (13/35 * 12/34 * 11/33 * 10/32) + (14/35 * 13/34 * 12/33 * 11/32)

Evaluate

P(Same type) = 0.0341

Hence, the probability that all 4 winners will select the same type of tree is 0.0341

b. The probability that 3 pine trees will be selected and the other tree will be a maple?

The probability is then calculated as:

P(3 pine and one maple) = 4 * P(Three maple and One Pine)

So, we have:

P(3 pine and one maple) = 4 * (13/35 * 12/34 * 11/33 * 13/32)

Evaluate

P(3 pine and one maple) = 0.0710

Hence, the probability that 3 pine trees will be selected and the other tree will be a maple is 0.0710

c. The probability that no fruit trees and 2 of each of the others will be selected?

The probability is then calculated as:

P(2 pine and 2 maple) = 4 * P(Two pine and Two maple)

So, we have:

P(2 pine and 2 maple) = 4 * (13/35 * 12/34 * 14/33 * 13/32)

Evaluate

P(2 pine and 2 maple) = 0.0904

Hence, the probability that no fruit trees and 2 of each of the others will be selected is 0.0904

Read more about probability at:

https://brainly.com/question/251701

Related Questions

What the best way to prepare for essay portion ?

Answers

How Do You Begin an Essay?

Decide on your essay type and topic. Sometimes, you will already have an assigned essay type or topic, so that will save you one step. ...

Brainstorm and research the topic you’ve chosen. Once you’ve chosen your topic, brainstorm all the different supporting ideas that you can talk about for the topic.

Develop your thesis statement. After you have brainstormed and researched, write down your thesis statement. ...

Write your outline. Once you have your thesis statement, you can start to prepare your outline. Many people skip the outline process, thinking it’s a waste of time.

Start writing. Using your outline, you can now begin writing your essay. Some writers choose to write their paragraphs in order, beginning with the hook.

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