Question

Let's compare two different raffles to see which ticket you should buy? A. Raffle 1: 800 raffle tickets are sold $2.00 each. There is one gran prize for $450 and two consolation prizes of $100 each that will be awarded. What is the expected value of one ticket? B. Raffle 2: 350 raffle tickets are sold for $2.00 each. There is one grand prize of $150 and three consolation prizes of $50 each. What is the expected value of one ticket?

Answer 1

Answer:

(a) The expected value is: $0.40625

(b) The expected value is: $0.4286

Step-by-step explanation:

Solving (a): Raffle 1

Given

$Tickets=800$

$Value = \ 2$ per ticket

$Grand\ Prize = \ 450$ ---- for 1

$Consolation = \ 100$ --- for 2

Required

The expected value of each ticket

First, calculate the total amount of the 800 tickets

$Amount = Tickets * Value$

$A_1 = 800 * \ 2$

$A_1 = \ 1600$

Next, calculate the total amount of the prizes

$Amount = Tickets * Value$

$A_2 = \ 450 * 1 +\ 100 * 2$

$A_2 = \ 450 +\ 200$

$A_2 = \ 650$

The expected value E(x) of 1 ticket is calculated as:

$E(x) = \frac{A_2}{A_1}$

$E(x) = \frac{\ 650}{\ 1600}$

$E(x) = \ 0.40625$

Solving (b): Raffle 2

Given

$Tickets=350$

$Value = \ 2$ per ticket

$Grand\ Prize = \ 150$ ---- for 1

$Consolation = \ 50$ --- for 3

Required

The expected value of each ticket

First, calculate the total amount of the 800 tickets

$Amount = Tickets * Value$

$A_1 = 350 * \ 2$

$A_1 = \ 700$

Next, calculate the total amount of the prizes

$Amount = Tickets * Value$

$A_2 = \ 150 * 1 +\ 50 * 3$

$A_2 = \ 150 +\ 150$

$A_2 = \ 300$

The expected value E(x) of 1 ticket is calculated as:

$E(x) = \frac{A_2}{A_1}$

$E(x) = \frac{\ 300}{\ 700}$

$E(x) = \ 0.4286$