Question

3. [Conditional probabilities] There are three boxes, each containing two coins. One box has two gold coins, another two silver coins, and the third has one gold and one silver coin. One of the three boxes is chosen at random and from that box a coin is drawn at random. Suppose that coin happens to be gold. What is the probability that the remaining coin in the box is also gold? Show your work.

Answer #1

suppose a box contains three coins. two are fair and one is a
coin with two tails. a coin is randomly selected from the box and
tossed once.
a) what is the probability that the result of the toss is a
tail?
b) Given the result of the toss is a tail, what is the
probability that the selected coin is the one with two tail?

2 boxes. In the first one, one 5 dolar coins, two 1 dolar
coins,,in the second there are 3 of 5 dolar coins and one of 1
dolar coin. A coin is taken from the first and putted in the second
box the second, and a coin is withdrawn from the second. if the one
withdrawn from the second box is 1 dolar coin what is the
probability that the money thrown from the first to the second is 5...

Suppose that we have a box that contains two coins:
A fair coin: ?(?)=?(?)=0.5 .
A two-headed coin: ?(?)=1 .
A coin is chosen at random from the box, i.e. either coin is
chosen with probability 1/2 , and tossed twice.
Conditioned on the identity of the coin, the two tosses are
independent.
Define the following events:
Event ? : first coin toss is ? .
Event ? : second coin toss is ? .
Event ? : two coin...

Suppose that we have a box that contains two coins:
A fair coin: ?(?)=?(?)=0.5 .
A two-headed coin: ?(?)=1 .
A coin is chosen at random from the box, i.e. either coin is
chosen with probability 1/2 , and tossed twice.
Conditioned on the identity of the coin, the two tosses are
independent.
Define the following events:
Event ? : first coin toss is ? .
Event ? : second coin toss is ? .
Event ? : two coin...

Donald has in his pocket three coins: two fair coins and a
two-headed coin. He selects one of the coins at random; when he
tosses it, it shows head. What is the probability that the selected
coin is a two-headed coin? Select one: a. 0.5 b. 0.75 c. 0.25 d.
0.333

Franklin has three coins, two fair coins (head on one side and
tail on the other side) and one two- headed coin. He randomly picks
one, flips it and gets a head. What is the probability that the
coin is a fair one?

A box contains 4 coins: coin1 has both sides tails; coin2 has
both sides heads; coin3 has both sides heads; coin4 is a regular
coin (one side heads, one side tails)
a) If we randomly choose one coin from the box and flip, what is
the probability we get heads?
b) Suppose we randomly choose a coin, flip, and get heads. What
is the probability that the coin that was chosen is the regular
coin?

Consider a box with three tickets numbered one to three. Suppose
a coin is tossed. If the coin toss results in a head, then two
tickets are drawn from the box with replacement. If the coin toss
results in a tail, then two tickets are drawn from the box without
replacement. Let A denote the event that the coin toss is a head.
Let B be the event that the sum of the tickets drawn is .
(1) Describe the...

We are given three coins: one has heads in both faces, the
second has tails in both faces, and the third has a head in one
face and a tail in the other. We choose a coin at random, toss it,
and the result is heads. What is the probability that the opposite
face is tails?

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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