Discrete Probability Distributions

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flora33

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A contractor must pay a $40,000 penatly 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 $350,000 before any penalty or bonus adjustment, how much can the buyer expect to pay for her new home when it is completed?

Using the discrete probability distribution:
P(0.2 or 0.3) = 0.5 or 50% chance the job is completed early or late. So, the buyer can expect to pay $350,000 when the home is completed. Am I correct on this?
 
flora33 said:
A contractor must pay a $40,000 penatly 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 $350,000 before any penalty or bonus adjustment, how much can the buyer expect to pay for her new home when it is completed?

Using the discrete probability distribution:
P(0.2 or 0.3) = 0.5 or 50% chance the job is completed early or late. So, the buyer can expect to pay $350,000 when the home is completed. Am I correct on this?

No -

you have consider three cases - early, in-time and late - and

consider (pay-off * probability) in each case and

add those up for final expected value.
Click to expand...
 
Ok, this is what I've come up with:

8 wks $360,000 x .3 = $108,000
16 wks $310,000 x .2 = $62,000
On time $350,000 x .5 = $175,000
Sum = $ 345,000

Am I closer?
 
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