Answer to Question #216685 in Statistics and Probability for Cat

Question

At a school raffle, students can purchase two types of tickets: Ticket A which costs $2.00 each, students can win the following prizes: twenty $10 Tim Horton's gift cards, twelve $15 Starbucks' gift cards, and five $30 Staples gift cards. Ticket B which costs $3.00 each, students can win the following prizes: three $25 Tim Horton's gift cards, and two $300 Staples gift card. Suppose there are only 600 of each types of tickets being sold.

a) Complete a probability distribution table for each ticket.

b) Determine which type of raffle ticket has greater value. Justify your answer.

Answer 1

Let X and Y be random variables denoting the value of ticket A and ticket B win in monetary terms.

Hence

P(X=$10) = 20/600 = 1/30=0.0333

P(X=$15) = 12/600 = 1/50=0.0200

P(X=$30) = 5/600 = 1/120=0.0083

P(X=$0) = (600-20-12-5)/600 = 563/600 =0.9383

$E(X) = (10\cdot 20 + 12\cdot15+5\cdot 30)/600 = 530/600 = 0.883$

Taking into account the cost of the ticket itself, we conclude that the total value of the ticket A is

0.883 - 2= - 1.117

P(Y=$25)=3/600 = 1/200 = 0.0050

P(Y=$300)=2/600 = 1/300 = 0.0033

P(Y=$0) = 595/600 = 119/120 = 0.9917

$E(Y)=3\cdot 25+2\cdot 300 = 675/600 =1.125$

Taking into account the cost of the ticket itself, we conclude that the total value of the ticket A is

1.125 - 3= - 1.875

Therefore, ticket A has greater value, than ticket B.