Question

Two coins: one is fair and one is not. Which coin has the higher entropy?

Answer #1

**Here' the answer to the question. please write back in
case you've doubts.**

When you toss a fair coin, for each side, the probability is .5,
and that' head or tails basically on the coin. So the total amount
of entropy is .5 times 1 (heads) + .5 times 1 (tails), or
**one bit.**

When you toss an unfair coin you know will land on tails every time or heads every time. There’s no surprise on th outcome of the unfair coin when it lands tails, therefore there are zero bits of entropy in the flip.

**Hence, an fair coin has higher entropy**

**Answer: Fair 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?

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?

Suppose I have two coins:
• Coin 1 is fair: H and T have the same probability
• Coin 2 is biased: H is twice as likely as T I select one of
the coins with equal probability and flip it.
If I obtained H, what is the probability that I chose coin
2?

Q1. I have two coins in my pocket, one is a fair coin,
the other has heads on both sides. I pick one at random, and
without looking at what it is, I toss it four times. I get four
heads. (HHHH).
(I) What is the probability that I picked the fair
coin?
(II) What is your answer if I got N heads in a row
rather than four?
Q2. A, B are cowboys. A hits every shot. A has...

A magician has 20 coins in his pocket. Twelve of these coins are
normal fair coins (with one head and one tail) and eight are
defective coins with heads on both sides. The magician randomly
draws a coin from his pocket and flips it. Given that the flipped
coin shows a head, what is the probability that it is
defective?
Select one:
4/7
8/20
1
1/2

Consider two coins, one fair and one unfair. The probability of
getting heads on a given flip of the unfair coin is 0.10. You are
given one of these coins and will gather information about your
coin by flipping it. Based on your flip results, you will infer
which of the coins you were given. At the end of the question,
which coin you were given will be revealed.
When you flip your coin, your result is based on a...

Part 1. Two fair coins are tossed and we are told that one
turned up “Heads”. What is the probability that the other turned up
“Tails”?
Part 2. Two fair coins are tossed, and we get to see only one,
which happened to turn up “Heads”. What is the probability that the
hidden coin turned up “Tails”?
*Remark This problem is really different from the previous
one!

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...

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