Question

Slim and Roy are flipping a unfair coin, where the coin has the chance to land on heads 65% of the time. Every time that the coin lands on heads, Slim gets 500 dollars from Roy, and Roy gets 500 dollars from Slim if the coin lands on tails. If the game is played 100 times (coin is flipped 100 times), what is the probability that Slim's winnings are $20,000 more than Roy's, where 'x' is strictly greater than 20,000 (x > 20,000)?

Answer #1

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?

Suppose you are flipping an unfair coin 10 times. Let p be the
probability of getting tails for said coin. Define X to be the
number of heads obtained.
(a.) Describe the sample space S.
(b.) Give the values x for X.
(c.) Find the likelihood of rolling exactly four heads.
(d.) Find fX(x) .

An unfair coin is flipped 3 times, heads is 4 times as likely to
occur than tails.
x= the number of heads.
Find the probability distribution, E(x), and σ(x).

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...

A certain “unfair” coin is one where the probability of a head
showing when flipped is 0.35 and the probability of a tail showing
is 0.65. An experiment consists of flipping 8 of these “unfair”
coins. Let the random variable x be the number of tails showing.
Determine the probability of 3 of the 8 coins showing tails.

One fair coin and two unfair coins where heads is 5 times as
likely as tails are put into a bag. One coin is drawn at random and
then flipped twice. If at least one of the flips was tails, what is
the probability an unfair coin was flipped?
Every day, Janet either takes the bus or drives her car to work.
She drives her car 30% of the time. When she drives her car, she
packs her lunch 70%...

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.

Consider the following game. You flip an unfair coin, with P(H)
= 1/4 and P(T) = 3/4, 100 times. Every time you flip a heads you
win $8, and every time you flip a tails you lose $3. Let X be the
amount of money you win/lose during the game. Justify your answers
and show all work. Compute E(X) andCompute V (X).

It is a slow day at Bunsen Motors, so since he has his
calculatorwarmed up, Clarence Bunsen decides to study his expected
utility functionmore closely.
a)Clarence first thinks about really big gambles. What if he bet
hisentire $10,000 on the toss of a coin, where he loses if heads
and wins iftails? Then if the coin came up heads, he would have 0
dollars and if itcame up tails, he would have $20,000.His expected
utility if he took thebet would...

1) At a lumber company, shelves are sold inȱȱ5 types of wood, 4
different widths and 3 different lengths. How many different types
of shelves could be ordered?
2) A shirt company has 5 designs each of which can be made with
short or long sleeves. There are 4 different colors available. How
many differentȱȱshirts are available from this company? Find the
indicated probability. Round your answer to 2 decimal places when
necessary.
3) A bag contains 6 red marbles,...

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