Question

A fishing company operates a search plane to find schools of fish in the ocean. Schools of fish are randomly located in the ocean. On average, there is one school of fish per 100,000 square miles of ocean. During any one day, the plane can search 10,000 square miles.

1. What is the expected number of schools of fish found in one
day of searching?

A. 0.1 B. 3 C. 1 D. 0.3

2. What is the probability of finding at least one school of fish in one day of searching?

3.What is the expected number of schools of fish found in three days of searching?

A. 0.3 B. 1 C. 3 D. 0.9

4. What is the probability of finding at least one school of fish during three days of searching?

5.What is the probability of finding 3 schools of fish during three days of searching?

6.What is the probability of finding one school of fish each day for three days in a row?

Answer #1

1)

expected number of schools of fish found in one day of searching =10000/100000=0.1

2)

probability of finding at least one school of fish in one day of searching =P(X>=1)=1-P(X=0)

=1-e^{-0.1} =0.0952

3)

expected number of schools of fish found in three days of searching =0.1*3 =0.3

4)

probability of finding at least one school of fish during three days of searching

=1-e^{-0.3} =0.2592

5)

probability of finding 3 schools of fish during three days of
searching =P(X=3)=e^{-0.3}*0.3^{3}/3!

=0.0033

6) probability of finding one school of fish each day for three days in a row

=(0.0952)*(0.0952)*(0.0952)=0.0009

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