Question

One thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and cash prizes are to be awarded as follows: 1 prize of $100, 3 prizes of $50, and 5 prizes of $20. What is the expected value of this raffle if you buy 1 ticket?

Now suppose some benefactor agrees to give every player $1000, regardless of the outcome of the raffle. What is the expected value of the game? What general principle is at work?

I know that the expected value without the benefactor is -$0.65 and then with the benefactor the expected value is $999.35. I am, however, confused as to what general principle is at work. Could you help me understand what this general principle is?

Answer #1

Expected value E[x]=μ which represent the overall average value
of the game

E[x]=∑ x*P(x) where

x=value of an outcome,

P(x)=probability of that outcome.

For given case, we sold 1000 tickets, out of which 1 prize of $100,
3 prizes of $50, and 5 prizes of $20.

So (1000-1-3-5 = 991) people will pay $1 (with probability of 991/1000 of losing) ,

and winners will get

(a) $100-$1=$99 with a probability of 1/1000 of winning).

(b) $50-$1=$49, with a probability of 3/1000 of winning).

(c) $20-$1=$19 with a probability of 5/1000 of winning).

Summing over the entire case

E[x]=(-1)*991/1000+(99)*1/1000+(49)*3/1000+(19)*5/1000

= -0.991 + 0.099 + 0.147 + 0.095

= -0.65 dollars

Five thousand tickets are sold at $1 each for a charity raffle.
Tickets are to be drawn at random and monetary prizes awarded as
follows: 1 prize of $700 , 3 prizes of $300 , 5 prizes of $50
, and 20 prizes of $5. What is the expected value of this raffle
if you buy 1 ticket?

1. One thousand tickets are sold at $1 each for a charity
raffle. Tickets are to be drawn at random and cash prizes are to be
awarded as follows: 1 prize of $100, 3 prizes of $50, and 5 prizes
of $20. What is the expected value of this raffle if you buy 1
ticket?
2. Suppose 10% of the high school students are late for
school.What is the probability that exactly 1 out of 5 students
will be late...

A charity is conducting a raffle to raise money. Tickets cost $2
each and it is expected that the charity will sell 8,000 tickets.
The winning raffle tickets are to be drawn at random and monetary
prizes awarded as follows: 1 prize of $500, 5 prizes of $100, and
30 prizes of $5.What is expected value and create a probability
distribution for this?

A charity raffle sells 2000 tickets for $1 each. Prizes are
awarded of one $100, four $50, and eight $25. Find the expected
value if you purchase 1 ticket. Your expected value should end up
negative since there are way more chances to not win than to win
one of the prizes. Expected value is calculated by multiplying
every possible outcome by its probability and then adding those
products. Let's break this down. a) In this case there are 2000...

You are participating in a raffle in which there will be 2000
tickets sold. Each ticket costs 5 dollars. There is 1 first prize,
a $100 gift certificate. 2 second prize $50 gift certificates. And
5 third prizes of $25. Use this information to answer the following
questions. Show your work.
a. What is the expected value of a single raffle ticket?
b. According to the mathematics, should you participate in the
raffle?
c. If you purchased 20 tickets, how...

b. Danny joined a charity event and there is a charity raffle.
The first prize was RM100000, the second prize was RM20000 with a
RM10000 third prize. The tickets were very expensive (RM2000) but
the total number of tickets was restricted to only 1000. This
contrasts with the usual situation of selling thousands of tickets
for a small nominal amount. Danny likes to support charities and
the prizes are very tempting.
If Danny buys a ticket, what is his expectation...

In a raffle where 2000 tickets are sold for $2 each, one first
prize of $600 and one second prize of $300 will be awarded. What is
the expected value of a single ticket in the raffle? Round your
answer to the nearest hundredth, and do not include a $ sign or the
word "dollars" in your response.

I buy one of 400 raffle tickets for $20. The sponsors then
randomly select 1 grand prize worth $600, then 2 second prizes
worth $200 each, and then 3 third prizes worth $50each. The
selections are made without replacement.
(a) Complete the probability distribution for this raffle. Give
your probabilities as a decimal (rounded to 4 decimal
places) or as a fraction.
Outcomes
P(x)
Win
Grand Prize
Win a
Second Prize
Win a
Third Prize
Win
Nothing
(b) Recognizing that...

9. A county fair is running a raffle. Tickets for the raffle
cost $1. If the raffle has a grand prize worth $50, five runner up
prizes worth $30, and fifty consolation prizes worth $5. Suppose
you purchase a ticket and the fair sells 600 tickets in total.
A.Create a probability distribution for the value of the ticket
purchased.
B .Find and interpret the mean value of the ticket.
C. Find the standard deviation for the value of the ticket

Lottery: I buy one of 200 raffle tickets for
$10. The sponsors then randomly select 1 grand prize worth $300, 2
second prizes worth $80 each, and 3 third prizes worth $40 each.
Below is the discrete probability distribution for this raffle.
Prize
P(x)
Grand
1/200
Second
2/200
Third
3/200
None
194/200
(a) Recognizing that I spent $10 to buy a ticket, determine the
expected value of this raffle to me as a player. Round your
answer to the nearest...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago