Question
In: Statistics and Probability
A box contains three fair coins and one biased coin. For the biased coin, the probability...
A box contains three fair coins and one biased coin. For the biased coin, the probability that any flip will result in a head is 1/3. Al draws two coins from the box, flips each of them once, observes an outcome of one head and one tail and returns the coins to the box. Bo then draws one coin from the box and flips it. The result is a tail. Determine the probability that neither Al nor Bo removed the biased coin from the box.
Solutions
orchestra answered 1 year agoRelated Solutions
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...
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...
There is a fair coin and a biased coin that flips heads with probability 1/4.You randomly...
There is a fair coin and a biased coin that flips heads with
probability 1/4.You randomly pick one of the coins and flip it
until you get a heads. Let X be the number of flips you need.
Compute E[X] and Var[X]
A jar contains 100 coins. One of the coins is a trick coin with heads on...
A jar contains 100 coins. One of the coins is a trick coin
with heads on both sides. The other 99 coins are ordinary coins
with heads probability .5. A coin is selected at random. (a) What
is the probability the coin selected is the trick coin? (b) The
coin selected is tossed 7 times, and it happens to land heads each
of those times. Now what is the probability it is the trick
coin?
1. One researcher believes a coin is “fair,” the other believes the coin is biased toward...
1. One researcher believes a coin is “fair,” the other
believes the coin is biased toward heads. The coin is tossed 21
times, yielding 16 heads. Indicate whether or not the first
researcher’s position is supported by the results. Use α =
.05.
2. Design a decision rule to test the hypothesis that a coin
is fair if a sample of 64 tosses of the coin is taken and if a
level of significance of (a) .05 and (b) .01...
1. Amy tosses 12 biased coins. Each coin comes up heads with probability 0.2. What is...
1. Amy tosses 12 biased coins. Each coin comes up heads with
probability 0.2. What is the probability that fewer than 3 of the
coins come up heads?
Answer: 0.5583
2. Amy shoots 27000 arrows at a target. Each arrow hits the
target (independently) with probability 0.2. What is the
probability that at most 2 of the first 15 arrows hit the
target?
Answer: 0.398
3. Amy tosses 19 biased coins. Each coin comes up heads with
probability 0.1. What...
Three fair coins are tossed simultaneously 10 times. Find the probability that "2 heads and one...
Three fair coins are tossed simultaneously 10 times. Find the
probability that "2 heads and one tail" will show up (a) at least
once and (b) at most once.
A biased coin is flipped 20 times in a row. The coin has a probability 0.75...
A biased coin is flipped 20 times in a row. The coin has a
probability 0.75 of showing Heads.
a. What’s the probability that you get exactly 8 Heads?
b. What’s the probability that you get exactly 8 Heads, given
that the first 2 flips show Heads?
c. What’s the probability that you never see the same result
consecutively( never see 2H or 2T in a row)
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