Question
In: Statistics and Probability
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?
Solutions
orchestra answered 1 year agoRelated Solutions
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...
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...
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...
Two fair coins and a fair die are tossed. Find the sample space of the experiment...
Two fair coins and a fair die are tossed. Find the sample space
of the
experiment (10 pts); Find the probabilities of the following
events:
A- ”the die shows 2 or 3” (5 pts);
B- ”one of the coins is head, the other - tail, and the die shows
an odd number” (5
pts).
Are the events A and B independent? (5 pts).
Give proofs.
One fair coin and two unfair coins where heads is 5 times as likely as 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?
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...
You have 100 coins, and 99 of them are fair (equal probability of heads or tails)....
You have 100 coins, and 99 of them are fair (equal probability
of heads or tails). One of them is weighted and has a 90%
probability of landing on heads. You randomly choose one of the 100
coins. Find the probability that it is a weighted coin, under the
following scenarios: (Hint: if your calculator can’t compute 100!,
R can, just type factorial(100))
(a) You flip it 10 times and lands on heads 10 times (b) You
flip it 10...
You are presented with 400 coins. 250 of them are fair coins, while the remaining 150...
You are presented with 400 coins. 250 of them are fair coins,
while the remaining 150 land heads with probability 0.65.
Part a: If you select 60 of the coins at random, what is the
probability that less than half of them are fair coins?
Part b: What is the probability that a randomly selected coin
flipped once will land heads?
Part c: Consider the following procedure:
1. Select one of the coins randomly.
2. Flip the coin.
3. Record...
You are presented with 400 coins. 250 of them are fair coins, while the remaining 150...
You are presented with 400 coins. 250 of them are fair coins,
while the remaining 150 land tails with probability 0.60.
Part a: If you select 60 of the coins at random, what is the
probability that less than half of them are fair coins?
Part b: What is the probability that a randomly selected coin
flipped once will land tails?
Part c: Consider the following procedure:
1. Select one of the coins randomly.
2. Flip the coin.
3. Record...
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