Question

Three coins are in a barrel with respective probabilites of
heads 0.3, 0.5, and 0.7. One coin is randomly chosen and flipped 10
times. Let *N* = # of heads obtained in the ten flips.

a. Find *P*(*N* = 0).

b. Find *P*(*N=n*), *n* = 0, 1, 2, ...,
10.

c. Does *N* have a binomial distribution? Explain.

d. If you win $1 for each heads that appears, and lose $1 for each tails, is this a fair game? Explain.

Answer #1

thank you

There are two coins and one of them will be chosen randomly and
flipped 10 times. When coin 1 is flipped, the probability that it
will land on heads is 0.50. When coin 2 is flipped, the probability
that it will land on heads is 0.75. What is the probability that
the coin lands on tails on exactly 4 of the 10 flips? Round
the answer to four decimal places.

When coin 1 is flipped, it lands on heads with probability
3
5
; when coin 2 is flipped it lands on heads with probability
4
5
.
(a)
If coin 1 is flipped 11 times, find the probability that it
lands on heads at least 9 times.
(b)
If one of the coins is randomly selected and flipped 10 times,
what is the probability that it lands on heads exactly 7
times?
(c)
In part (b), given that the...

You are given 5 to 2 odds against tossing three heads with
three coins, meaning you win $5 if you succeed and you lose $2
if you fail. Find the expected value (to you) of the game. Would
you expect to win or lose money in 1 game? In 100 games? Explain.
Find the expected value (to you) for the game.

You are given 3 to 2 odds against tossing three heads with
three? coins, meaning you win ?$3 if you succeed and you lose ?$2
if you fail. Find the expected value? (to you) of the game. Would
you expect to win or lose money in 1? game? In 100? games?
Explain.

Deriving fair coin flips from biased coins: From coins with
uneven heads/tails probabilities construct an experiment for which
there are two disjoint events, with equal probabilities, that we
call "heads" and "tails".
a. given c1 and c2, where c1 lands heads up with probability 2/3
and c2 lands heads up with probability 1/4, construct a "fair coin
flip" experiment.
b. given one coin with unknown probability p of landing heads
up, where 0 < p < 1, construct a "fair...

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 ∈...

coin 1 has probability 0.7 of coming up heads, and coin 2 has
probability of 0.6 of coming up heads. we flip a coin each day. if
the coin flipped today comes up head, then we select coin 1 to flip
tomorrow, and if it comes up tail, then we select coin 2 to flip
tomorrow. find the following:
a) the transition probability matrix P
b) in a long run, what percentage of the results are heads?
c) if the...

you are given 4 to 1 odds against three heads with three coins ,
meaning you win $4 if you succeed and you lose $1 if you fail. find
expected value of game . what would you expect to win in 1 game or
100 games?
I understand the formula for finding the expected value . what i
am having trouble with is putting the information into the equation
regarding where it gets
put into the equation

Consider two coins, one fair and one unfair. The probability of
getting heads on a given flip of the unfair coin is 0.10. You are
given one of these coins and will gather information about your
coin by flipping it. Based on your flip results, you will infer
which of the coins you were given. At the end of the question,
which coin you were given will be revealed.
When you flip your coin, your result is based on a...

A box contains 2 coins: one has probability 1/2 of heads, while
the other has unknown probability p, 0<=p<=1, of heads. A
coin is selected at random and flipped. It is then replaced in the
box, and this entire procedure is repeated another time. If 2 heads
are observed, what is the value of the maximum likelihood estimator
of p?
A) 1/4
B) 1/2
C) 3/4
D) 1
E) doesn't exist

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