2017 NYJC J2 MYE P2 Q8

An experienced farmer rear chickens in a small and large farm.

1. On a particular day, \(15\) eggs are laid in his small farm and the farmer identified that only five are fertilised for hatching. Four eggs are selected at random without replacement for testing. Find the probability that at least one fertilised egg will be selected.[3]
2. In his large farm, a large number of eggs are laid by the chickens daily and \(20\%\) of the eggs are fertilised. Every day, \(15\) eggs are selected randomly and independently without replacement for testing.
   1. Give a reason why the number of fertilised eggs can be modelled using a Binomial distribution. Find the probability that at least five fertilised eggs will be selected on a particular day.[3]
   2. Find the probability that in a period of \(30\) days, there are \(20\) days with at most four fertilised eggs selected in a day.[2]