Question 1 - A-Level Maths

Exam Board	WJEC
Module	Further Unit 2 (Further Unit 2)
Year	2022
Session	June
Topic	Discrete Probability Distributions
Type	One unknown from sum constraint only

The probability distribution for the prize money, \(\pounds X\) per ticket, in a local fundraising lottery is shown below.

\(x\)	0	2	100	1000
\(\mathrm { P } ( X = x )\)	0.9	0.09	\(p\)	0.0001

Calculate the value of \(p\).
Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).
1. What is the minimum lottery ticket price that the organiser should set in order to make a profit in the long run?
2. Suggest why, in practice, people would be prepared to pay more than this minimum price.