In: Statistics and Probability
A biologist needs at least 4 mature specimens of a certain
plant. The plant needs a year to
reach maturity; once a seed is planted, any plant will survive for
the year with probability
1/1000 (Independently of other plants). The biologist plants 2000
seeds. A year is deemed a
success if 4 or more plants from these seeds reach maturity.
a. Write down the exact expression for the probability that the
biologist will indeed end up
with at least 4 mature plants.
b. Write down the relevant approximate expression for the
probability from (a). Justify
briefly the approximation.
c. The biologist plans to do this year after year. What is the
approximate probability that he
has at least 3 success in 8 years?