Question

You have the opportunity to invest $20 , with an uncertain return. To simulate uncertainty, we will use a deck of four playing cards consisting of two aces and two kings. The deck has been shuffled and placed face down on the table in front of you. You will now draw two cards, one after the other:

If you draw two aces, you will receive $60

If you draw an ace and a king, you will receive $30

if you draw two kings, you will have to pay an additional $18 and receive nothing

a) Let's assume that you are risk neutral for these dollar amounts. What is the expected value of the investment?

b) A special risk mitigation opportunity is available, for $5. If you buy the opportunity, you will receive $6 (andnot have to pay $18) if the outcome is two kings. Should you buy it? Explain. c) An expert card dealer can tell you what the first card is. He will charge $6 for the information. Should you pay for the information?

Answer #1

P(2 aces) = 2/4*1/3 = 1/6

P(1 ace, 1 king) = 2*1/2*2/3 = 2/3

P(2 king) = 1/6

a) Expected value = 1/6*60 + 2/3*30 - 18*1/6 = $27

Expected return = 27-20 = $7

b) Now investment = 20+5 = $25

Now, Expected value = 1/6*60 + 2/3*30 + 6*1/6 = $31

Expected return = 31-25 = $6

Now return is lower so we should not buy it.

c) If expert card dealer can tell you what the first card is, then probabilities changes:

P(2 aces) = 1/2*2/3 = 1/3

P(1 ace, 1 king) = 2*1/2*2/3 = 2/3

P(2 king) = 1/3

Now, Expected value = 1/3*60 + 2/3*30 - 18*1/3 = $34

Expected return = 34-20 -6(expert charge) = $8

This is higher return hence we should pay for this information.

he following question involves a standard deck of 52 playing
cards. In such a deck of cards there are four suits of 13 cards
each. The four suits are: hearts, diamonds, clubs, and spades. The
26 cards included in hearts and diamonds are red. The 26 cards
included in clubs and spades are black. The 13 cards in each suit
are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This
means there are four...

The following question involves a standard deck of 52 playing
cards. In such a deck of cards there are four suits of 13 cards
each. The four suits are: hearts, diamonds, clubs, and spades. The
26 cards included in hearts and diamonds are red. The 26 cards
included in clubs and spades are black. The 13 cards in each suit
are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This
means there are four...

Suppose you have a 52-card deck.
a) what is the probability of selecting two kings from the
deck?
b) what is the probability of selecting two queens
c) what is the probability of selecting a king, and then and
ace, and then a ten?

Suppose you are about to draw two cards at a random from a deck
of playing cards. Note that
there are 52 cards in a deck. Find the following
probabilities.
a. What is the probability of getting a Jack and then a King
(with replacement)?
b. What is the probability of getting a Heart or Jack and then a
2 (with replacement)?
c. What is the probability of getting an Ace and then a Queen
(without replacement)?
d. What is...

Suppose that we draw two cards from a standard deck of 52
playing cards, where ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen
and king each appear four times (once in each suit). Suppose that
it is equally likely that we draw any card remaining in the
deck.
Let X be the value of the first card, where we count aces as 1,
jacks as 11, queens as 12, and kings as 13. Let Y be...

The following question involves a standard deck of 52 playing
cards. In such a deck of cards there are four suits of 13 cards
each. The four suits are: hearts, diamonds, clubs, and spades. The
26 cards included in hearts and diamonds are red. The 26 cards
included in clubs and spades are black. The 13 cards in each suit
are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This
means there are four...

An online card game uses a deck of 32 cards containing 4 Aces, 8
Kings, 16 Queens, 2 Jacks and 2 Tens. In each round of the game the
cards are shuffled, the players make a bet about what type of card
will be drawn, then a single card is drawn and the winners are paid
off. The drawn card is reinserted into the deck before the next
round begins.
i. How much information does a player receive when she...

You pay $20 to play a game. You choose a card from a standard
deck of cards plus two jokers (total of 54 cards) at random. If you
pick a joker you get $200; if you pick an ace you get $50; if you
get a face card you get $25. Otherwise you receive nothing.
Calculate the expected value of this game.

One of the ways that players can increase their odds of winning
at blackjack is by keeping track of what cards have been played,
and using that information to decide what to do. To counteract this
strategy, casinos usually run games with 6 to 8 decks shuffled
together and machines to continuously shuffle the cards, making it
all but impossible to count the cards. As a result, when
calculating odds for casino games of blackjack we can make the
simplifying...

You have an opportunity to invest in a deal that will make
yearly payments forever. These payments will grow at a rate of 5%
per year. You will receive your first payment of 8,000 one year
from today. Due to the risks associated with this investment, you
will require a return of 15%. How much are you willing to pay for
this deal today?
Select one:
a. 85,000
b. 80,000
c. 87,500
d. 100,000
.
The firm makes no use...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 13 minutes ago

asked 18 minutes ago

asked 25 minutes ago

asked 32 minutes ago

asked 39 minutes ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago