Question

Suppose that you get the opportunity to play a coin flipping game where if your first flip is a “head”, then you get to flip five more times; otherwise you only get to flip two more times.

Assuming that the coin is fair and that each flip is independent, what is the expected total number of “heads”?

Answer #1

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A game consists of flipping a fair coin twice and counting the
number of heads that appear. The distribution for the number of
heads, X, is given by: P(X = 0) = 1/4; P(X =1) = 1/2; P(X = 2) =
1/4. A player receives $0 for no heads, $2 for 1 head, and $5 for 2
heads (there is no cost to play the game). Calculate the expected
amount of winnings ($).

in which case are you likely to get all heads from flipping a ,
if you flip a fair coin twice or if you flip a coin ten times

You are playing a game that involves flipping a coin, but you
begin to suspect that the coin is not fair (P(heads) = P(tails) =
0.5). In fact, your current estimate of P(heads) = 0.59, based on
100 coin flips. Is this enough information to say that the coin is
not fair with 95% confidence? If not, how many more coin flips
would be required (assuming the P(heads) remains the same)?

Suppose you and your roommate use a coin-flipping app to decide
who has to take out the trash: heads you take out the trash, tails
your roommate does. After losing a number of flips, you start to
wonder if the coin-flipping app really is totally random, or if it
is biased in one direction or the other.
To be fair to your roommate, you wish to test whether the app is
biased in either direction, and thus a two-tailed test...

You are flipping a fair coin with one side heads, and the other
tails. You flip it 30 times.
a) What probability distribution would the above most closely
resemble?
b) If 8 out of 30 flips were heads, what is the probability of
the next flip coming up heads?
c) What is the probability that out of 30 flips, not more than
15 come up heads?
d) What is the probability that at least 15 out 30 flips are
heads?...

A game is played by first flipping a fair coin, then rolling a
die multiple times. If the coin lands heads, then die A is to be
used; if the coin lands tails, then die B is to be used. Die A has
4 red and 2 white faces, whereas die B has 2 red and 4 white faces.
If the first two throws result in red, what is the probability that
the coin landed on heads?

A player is given the choice to play this game. The player flips
a coin until they get the first Heads. Points are awarded based on
how many flips it took:
1 flip (the very first flip is Heads): 2 points
2 flips (the second flip was the first Heads): 4 points
3 flips (the third flip was the first Heads): 8 points
4 flips (the fourth flip was the first Heads): 16 points
and so on. If the player...

a) Michael and Christine play a game where Michael selects a
number from the set {1,2,3,4,....8}. He receives N dollars if the
card selected is even; otherwise, Michael pays Christine two
dollars. Determine the value of N if the game is to be fair.
b) A biased coin lands heads with probability 1/4 . The coin is
flipped until either heads or tails has occurred two times in a
row. Find the expected number of flips.

We play a game where we throw a coin at most 4 times. If we get
2 heads at any point, then we win the game. If we do not get 2
heads after 4 tosses, then we loose the game. For example, HT H, is
a winning case, while T HT T is a losing one. We define an
indicator random variable X as the win from this game.
You make a decision that after you loose 3 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)...

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