Question
In: Statistics and Probability
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 pretty sure it’s the fair coin?
Explain your answer.
Solutions
orchestra answered 2 years agoRelated Solutions
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...
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...
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...
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...
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?
In your pocket, you have seven coins: 2 ten cent pieces, 2 fifty cent pieces, 2...
In your pocket, you have seven coins: 2 ten cent pieces, 2 fifty
cent pieces, 2 one dollar pieces and 1 two dollar piece. You
simultaneously choose two coins from your pocket (before you can
feel the difference between any of them). Let ? represent the value
of the two coins (in cents) that you select from the pocket. a)
NEATLY Create a probability distribution for ? and ?(? = ?). HINT:
Consider using a tree diagram to represent the...
coins have a mean of 2.5 g 32 coin sample the sample coins have a mean...
coins have a mean of 2.5 g
32 coin sample
the sample coins have a mean weight of 2.49496
standard deviation of 0.01722g with a 0.05 significance level
to test the claim this sample from s population with a mean weight
of 2.5 gm
give test statistic and p value
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?
Losing a coin. You begin the day carrying 2 nickels and 1 dime in your pocket....
Losing a coin. You begin the day carrying 2
nickels and 1 dime in your pocket. Sadly, your pocket has a hole.
Very sadly, at the end of the day, one of the 3 coins has fallen
out. Each of the three coins has an equal probability of falling
out. In the evening, you reach into your pocket and pull out one of
the two remaining coins, each of which has an equal probability of
being chosen. The coin you...
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