A farmer has 400 feet of fencing she would like to use to make a rectangular enclosure. She would like to maximize the area of t
he enclosure. The graph below shows the square footage of the enclosure,
depending on the length of it.
Enclosure with 400-foot Perimeter
12,000
10,000
8,000
Area (square feet)
6,000
4,000
2,000
0
200
50 100 150
Length of Enclosure (feet)
depending on the length of it.
Enclosure with 400-foot Perimeter
12,000
10,000
8,000
Area (square feet)
6,000
4,000
2,000
0
200
50 100 150
Length of Enclosure (feet)
1 answer:
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(a)
The sample space is a set whose elements are all the possible outcomes for the experiment. Since we will extract one of the months of the years, the sample space is the set composed by all the 12 months:
(b)
An event is a subset of the sample space. Events are often defined by their properties. In this example, the event E is the subset of the sample space defined as
So, we have
(c)
If all outcomes have equal probability, then the probability of an event is the ratio bewteen its cardinality, and the cardinality of the whole sample space:
In words, since there are three months beginning with J out of 12 months, we have a probability of 3 over 12 to pick a month starting with J, which simplifies to 1 over 4.