2022 EJC P2 Q7
In a carnival lucky dip game, a game master places n consolation tickets, $m$ blank tickets, and one golden ticket into a box. A contestant taking part in the game would pay $\$1$ to draw two tickets from the box. They would then be awarded $\$1$ for each consolation ticket drawn, and $\$10$ for the golden ticket if it is drawn. Nothing is awarded for the blank tickets drawn. Let $\$W$ represent the total amount awarded to a contestant after one game.
(a)
Show that $\text{P}\left( W=1 \right)=\frac{2nm}{\left( n+m+1 \right)\left( n+m \right)}$, and determine the probability distribution of $W$.
[4]
(b)
By considering $\text{E}\left( W \right)$, show that if the game master expects to make a profit from the lucky dip game, then $m-n>19$.
[3]
The game master then decides to run the game with $10$ consolation tickets and $40$ blank tickets. He is also issued with carnival lucky draw tickets to give away, and gives each contestant $Y$ lucky draw tickets after the game, where $Y=\left| W-4 \right|$.
(c)
Find $\text{E}\left( Y \right)$ and $\text{Var}\left( Y \right)$.
[2]
Suggested Video Solutions
Share with your friends!
Continue reading
Maximizing June Holidays: Is Joining a Crash Course Necessary?
As June holidays approach, students find themselves at a crucial juncture in their academic journey. With the semester winding down and exams looming on the horizon, the pressure to excel
5 Exam Preparation Tips: How We Help Students Excel in Exams
In the ever-evolving landscape of education, where academic success is often measured by performance in exams, the need for effective test preparation has never been more critical. Students face a
List MF 27
What is the MF 27? The MF 27, set to replace the MF 26 from 2025, is a comprehensive formula sheet developed by the Ministry of Education Singapore in collaboration