A farmer must decide whether to take protective action to limit damage to his grapefruit crop in the event that the overnight temperature falls to a level well below freezing. If the temperature drops too low he runs the risk of losing his entire crop, valued at $75,000. Based on the National Weather Service, the probability of such a temperature drop is 60%. He can insulate his crop by spraying water on all the trees, which will cost $20,000. This action might succeed in protecting the crop, with the following possible outcomes: Probability Damage 0.30 $0 0.15 $5,000 0.10 $10,000 0.15 $15,000 0.30 $20,000 Find the highest cost of insulating the grapefruits for which the farmer prefers to insulate his crop. Report your answer in thousands of dollars (if your answer is $100,000, enter 100).
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
A farmer must decide whether to take protective action to limit damage to his grapefruit crop in the
|
Probability |
Damage |
|
0.30 |
$0 |
|
0.15 |
$5,000 |
|
0.10 |
$10,000 |
|
0.15 |
$15,000 |
|
0.30 |
$20,000 |
Find the highest cost of insulating the grapefruits for which the farmer prefers to insulate his crop. Report your answer in thousands of dollars (if your answer is $100,000, enter 100).
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