1 problem found
The national lottery of Ruritania is based on the positive integers from \(1\) to \(N\), where \(N\) is very large and fixed. Tickets cost \(\pounds1\) each. For each ticket purchased, the punter (i.e. the purchaser) chooses a number from \(1\) to \(N\). The winning number is chosen at random, and the jackpot is shared equally amongst those punters who chose the winning number. A syndicate decides to buy \(N\) tickets, choosing every number once to be sure of winning a share of the jackpot. The total number of tickets purchased in this draw is \(3.8N\) and the jackpot is \(\pounds W\). Assuming that the non-syndicate punters choose their numbers independently and at random, find the most probable number of winning tickets and show that the expected net loss of the syndicate is approximately \[ N\; - \; %\textstyle{ \frac{5 \big(1- e^{-2.8}\big)}{14} \;W\;. \]