Question

A casino offers you a deal, in you bet $20:

Flip a coin and if you get TAILS, you win $40

Flip a coin 2 TIMES and if you get 2 TAILS, you win $400

Flip a coin 3 TIMES and if you get 3 TAILS, you win $1000

Flip a coin 10 TIMES and if you get 10 TAILS, you win $40,000

Which offer would you pick and explain your answer!

Answer #1

Suppose you can place a bet in the following game. You flip a
fair coin (50-50 chance it lands heads). If it lands heads, you get
4 dollars, if it lands tails, you pay 1 dollar. This is the only
bet you can make. If you don't make the bet you will neither gain
nor lose money. What is the expected utility of not placing the
bet?

If you flip a fair coin and get heads 10 times in a row, what is
the chance of getting tails on the next flip? Explain.

Flip a coin 13 times. If you get 7 tails or less, I will pay you
$37. Otherwise you pay me $91. Step 2 of 2: If you played this game
968 times how much would you expect to win or lose? Round your
answer to two decimal places. Losses must be entered as
negative.

Question 3: You are
given a fair coin. You flip this coin twice; the two flips are
independent. For each heads, you win 3 dollars, whereas for each
tails, you lose 2 dollars. Consider the random variable
X = the amount of money that you
win.
– Use the definition of expected value
to determine E(X).
– Use the linearity of expectation to
determineE(X).
You flip this coin 99 times; these
flips are mutually independent. For each heads, you win...

If you flip a coin 56 times, how many times would you expect to
get either 3 heads or 3 tails?

4. The Casino Control Commission takes a coin from a casino it
suspects to be unfair. They flip the coin 10 times and lands on
heads 8 times.
(a) What is the probability that a fair coin would land on heads
at least 8 times?
(b) Based on your answer to the last question, do you think the
coin is unfair? Explain.
5. Every day, Janet either takes the bus or drives her car to
work. She drives her car...

You have R500. You are approached by a person that offers you a
game. You flip a coin and if it’s heads you win R450 and if it’s
tails you win R50. He says it costs R250 to play each round. You
decide to play 2 rounds (so you spend your full R500). Calculate
the expected return and standard deviation of playing the game 2
times.

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)...

If I tell you that I have a coin, but it is a special coin. In
that, I mean that it is not a 50/50 coin. However, I don't know how
likely it is for it to land on heads (or tails). So we decide to
flip it 10 times and we get 40% heads (which is 0.40 as a
proportion). Are you willing to say that it is a 40/60 coin? Why or
why not?
after we flipped it...

You select a coin at random: 2/3 of the coins are unfair, 1/3 of
the coins are fair. The fair coins are equally likely to flip heads
or tails. The unfair coins flip heads 3/4 of the times, and tails
1/4 of the times. You flip the selected coin and get heads or
tails. Find (1) the probability that the selected coin is fair
given the flip is heads, (2) the probability that the selected coin
is fair given the...

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