Question

Consider a game in which a coin will be flipped three times. For each heads you will be paid $100. Assume that the coin comes up heads with probability ⅔.

a. Construct a table of the possibilities and probabilities in this game. The table below gives you a hint on how to do this and shows you that there are now eight possible outcomes. (3 points)

b. Compute the expected value of the game. (2 points)

c. How much would you be willing to pay to play this game? (3 points)

d. Consider the effect of a change in the game so that if tails comes up two times in a row, you get nothing. How would your answers to parts a-c change? (2 points)

Answer #1

A coin is flipped. If a heads is flipped, then the coin is
flipped 4 more times and the number of heads flipped is noted;
otherwise (i.e., a tails is flipped on the initial flip), then the
coin is flipped 2 more times and the result of each flip (i.e.,
heads or tails) is noted successively. How many possible outcomes
are in the sample space of this experiment?

You play a coin flip game where you win NOTHING if the coin
comes up heads or win $1,000 if the coin comes up tails. Assume a
fair coin is used. Which of the following is TRUE?
Group of answer choices
a. A risk-seeking person would be willing to accept a cash
payment of $500 to forgo (i.e. pass up) playing the game.
b. A risk neutral person might accept a cash payment of $400 to
forgo (i.e. pass up)...

Suppose you flipped an honest coin ten times and heads
came up eight times. You are about to toss the coin another ten
times. Using adaptive expectations, how many heads do you expect?
Based on rational expectations, how many heads do you expect?

Suppose that an unfair coin comes up heads 52.2% of the time.
The coin is flipped a total of 19 times.
a) What is the probability that you get exactly 9 tails?
b) What is the probability that you get at most 17 heads?

Consider this game: each person flips a coin once, if it is
heads, the person gets $20, and if it is tails, the person loses
$10.
For a group of 5, each person flips a coin once and
plays the game described above. What is the probability that this
group of 5 will lose money as a group? (Hint: list all possible
outcomes for this group and sum up the probabilities of outcomes
with a total loss.)

java
beginner level
NO ARRAYS in program
Flip a coin (Assignment)
How many times in a row can you flip a coin and gets heads?
Use the random number generator to simulate the flipping of the
coin. 0 means heads, 1 means tails.
Start a loop,
flip it, if heads, count it and keep flipping.
If tails, stop the loop.
Display the number of times in a row that heads came up.
Once this is working, wrap a while loop...

A coin with two sides, heads and tails, is flipped 100 times.
What is the probability that a "heads" will come up exactly 60
times?
Submit your answer as a decimal fraction (range: 0 to
1) to five (5) decimal places.

A coin is flipped 1000 times and you earn 3 dollars every time
the coin shows “Heads” and you give away 2 dollars when the coin
shows “Tails”. Define Y = Income after 1000 coin tosses. Then, Y ∼
Binomial distribution. Is this true or false and why?

question 3.
A coin has two sides, Heads and Tails. When flipped it comes up
Heads with an unknown probability p and Tails with probability q =
1−p. Let ˆp be the proportion of times it comes up Heads after n
flips. Using Normal approximation, find n so that |p−pˆ| ≤ 0.01
with probability approximately 95% (regardless of the actual value
of p). You may use the following facts: Φ(−2, 2) = 95% pq ≤ 1/4 for
any p ∈...

Casinos in Atlantic City are looking to offer a special coin
flip game where the player wins $4,000 if the coin comes up heads
and loses $1,000 if the coin comes up tails. Assume a fair coin is
used. Which statement below BEST describes the new coin flip
game?
A. All statements are true.
B. A risk averse person would pay less than $1,500 to play this
game.
C. A risk neutral person would be willing to pay $1,500 to...

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