Question
In: Statistics and Probability
In a pocket, Peter has 3 fair coins (which have one head and one tail on...
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In a pocket, Peter has 3 fair coins (which have one head and one tail on each side) and 7 unfair coins (which have heads on both sides). Peter randomly picks a coin from the pocket and flips the coin twice.
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(a) What is the probability that a head comes up on both flips?
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(b) If it’s known that a head comes up on the first two flips, when Peter flips the coin again, what is the probability that a head comes up on the third flip?
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Solutions
orchestra answered 2 years agoRelated Solutions
In a pocket, Peter has 3 fair coins (which have one head and one tail on...
In a pocket, Peter has 3 fair coins (which have one head and one
tail on each side) and 7 unfair coins (which have heads on both
sides). Peter randomly picks a coin from the pocket and flips the
coin twice.
(a) What is the probability that a head comes up on both
flips?
(b) If it’s known that a head comes up on the first two flips,
when Peter flips the coin again, what is the probability that a...
You have 3 coins that look identical, but one is not a fair coin. The probability...
You have 3 coins that look identical, but one is not a fair
coin. The probability the unfair coin show heads when tossed is
3/4, the other two coins are fair and have probability 1/2 of
showing heads when tossed.
You pick one of three coins uniformly at random and toss it n
times, (where n is an arbitrary fixed positive integer).
Let Y be the number of times the coin shows heads. Let X be the
probability the coin...
You have two coins, one of which you know to be fair and the other of...
You have two coins, one of which you know to be fair and the
other of which has a probability of turning up heads of 0.7, but
you can’t tell which one is which. You choose one coin at random
and flip it ten times getting an equal number of heads and tails.
What is the probability that you chose the unfair coin?
A person has 5 coins in his pocket. Two have both sides being heads, one has...
A person has 5 coins in his pocket. Two have both sides being
heads, one has both sides being tails, and two are normal. The
coins cannot be distinguished unless one looks at them.
a) The person closes his eyes, picks a coin from pocket at
random, and tosses it. What is the probability that the down-side
of the coin is heads?
b) He opens his eyes and sees that the up-side of the coin is
heads. What is the...
Conditional probability You have two coins in your pocket. One is a regular coin and the...
Conditional probability
You have two coins in your pocket. One is a regular coin and the
other is a weighted coin that has a 75% chance of landing heads up.
You can’t tell the coins apart by inspecting them. You take a coin
out of your pocket and toss it. It lands heads up.
a. What is the probability that the coin is the fair coin?
b. How many times would you decide to flip the coin before you
are...
Suppose you have a bag of 100 coins. Ninety of them are fair coins, which is...
Suppose you have a bag of 100 coins. Ninety of them are fair
coins, which is P(H) = P(T) = 1/2. The other 10 coins are biased ,
they have tail (T) on both sides. Let X = {X1, X2, · · · , X100} be
a random variable denoting the the total number of heads in the 100
coin flips.
a. How many possible values X can take? For example, if one
tosses two fair coins, the number of...
A con man has 3 coins. One coin has been specially made and has a head on each side. A second coin has..
A con man has 3 coins. One coin has been specially made and has a head on each side. A second coin has been specially made, and on each side it has a tail. Finally, a third coin has a head and a tail on it. All coins are of the same denomination. The con man places the 3 coins in his pocket, selects one, and shows you one side. It is heads. He is willing to bet you even...
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...
A box contains 5 fair coins, 4 coins that land heads with
probability 1/3 , and 1 coin that lands heads with probability 1/4
. A coin is taken from the box at random and flipped repeatedly
until it has landed heads three times. Let X be the number of times
that the coin is flipped and Y be the probability that the coin
lands heads.
(a) Find the random variables E(X|Y ) and var(X|Y ) in terms of
Y...
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...
A box contains 5 fair coins, 4 coins that land heads with
probability 1/3 , and 1 coin that lands heads with probability 1/4
. A coin is taken from the box at random and flipped repeatedly
until it has landed heads three times. Let X be the number of times
that the coin is flipped and Y be the probability that the coin
lands heads.
(a) Find the random variables E(X|Y ) and var(X|Y ) in terms of
Y...
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...
A box contains 5 fair coins, 4 coins that land heads with
probability 1/3 , and 1 coin that lands heads with probability 1/4
. A coin is taken from the box at random and flipped repeatedly
until it has landed heads three times. Let X be the number of times
that the coin is flipped and Y be the probability that the coin
lands heads.
(a) Find the random variables E(X|Y ) and var(X|Y ) in terms of
Y...
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