Question

Mathew buys a single ticket for $8 out of a lottery of 1000 tickets where the prize for the one winning is to be $800. How much is the expected earning per ticket?

Answer 1

Given:

The number of tickets = 1000

Mathew buys a single ticket for $8

Winning price = $800

To find:

The expected earning per ticket.

Solution:

It is given that the total number of tickets is 1000. So, the probability of winning is:

$P(Winning)=\dfrac{1}{1000}$

The probability of losing is:

$P(losing)=\dfrac{999}{1000}$

The expected earning per ticket is:

$E(x)=800\times P(Winning)-8\times P(losing)$

$E(x)=800\times \dfrac{1}{1000}-8\times \dfrac{999}{1000}$

$E(x)=\dfrac{800}{1000}-\dfrac{7992}{1000}$

$E(x)=\dfrac{800-7992}{1000}$

$E(x)=\dfrac{-7192}{1000}$

$E(x)=-7.192$

Therefore, the expected earning per ticket is -7.192. Here, negative sign means loss of $7.192.