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.)

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MrRoyal MrRoyal · Answer 1 · 2022-04-18T16:44:00+02:00

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

The distribution of the trees are:

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

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

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