A biologist needs at least $3$ mature specimens of 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 $3000$ seeds. A year is deemed a success if three 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 $3$ mature plants.
