A contractor must pay a $40,000 penalty if construction of an expensive home requires more than 16 weeks. He will receive a bonus of $10,000 if the home is completed within 8 weeks. Based on experience with this type of project, the contractor feels there is a 0.2 chance the home will require more than 16 weeks for completion, and there is a 0.3 chance it will be finished within 8 weeks. If the price of the home is $550,000 before any penalty or bonus adjustment, how much can the buyer expect to pay for her new home when it is completed?

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Patch

Business

20 February, 12:47

A contractor must pay a $40,000 penalty if construction of an expensive home requires more than 16 weeks. He will receive a bonus of $10,000 if the home is completed within 8 weeks. Based on experience with this type of project, the contractor feels there is a 0.2 chance the home will require more than 16 weeks for completion, and there is a 0.3 chance it will be finished within 8 weeks. If the price of the home is $550,000 before any penalty or bonus adjustment, how much can the buyer expect to pay for her new home when it is completed?

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Johnathon Herman · Answer 1

It will expect to pay 545,000 dollars

Explanation:

We will calculate the probabilities:

outcome x probability

(40,000) x 0.2 = (8,000) penalty

10,000 x 0.3 = 3,000 bonus

0 x 0.5 = 0 netiher

(5,000) expected

NOTE: the method will only work if the probabilities add up to one, so the remainder 0.5 will be assing to the timeframe within 8 ann 16 week on which there is no bonus or penalty.

list price: 550,000 + probability outcome: (5,000) = 545,000