What is the entropy of flipping a biased coin?

Independent fair coin flips have an entropy of 1 bit per flip. A source that always generates a long string of B’s has an entropy of 0, since the next character will always be a ‘B’. The entropy rate of a data source means the average number of bits per symbol needed to encode it.

How do you convert a biased coin to unbiased?

57. How can you use a biased coin to make an unbiased decision? That is to say the coin does not give heads or tales with equal probability….Von Neumann wrote it like this:

1. Toss the coin twice.
2. If the results match, start over, forgetting both results.
3. If the results differ, use the first result, forgetting the second.

How many flips are needed to detect a biased coin?

It is of course impossible to rule out arbitrarily small deviations from fairness such as might be expected to affect only one flip in a lifetime of flipping; also it is always possible for an unfair (or “biased”) coin to happen to turn up exactly 10 heads in 20 flips.

When a biased coin is tossed the probability of getting a tail is 1/4 if the coin is tossed two times what is the probability of getting two heads?

1/4 =0.25 = 25\%. There are four possible outcomes:. HH, HT, TH, TT (where H and T represent heads and tails respectively). If the coin is fair, then each of the outcomes has a probability of 1/4 = 0.25 = 25\%.

What is the entropy of a coin?

Digesting Entropy Mathematically In the case of a coin, we have heads (1) or tails (0). So, the entropy for the fair coin case comes out to be 1. Utter uncertainty (remember, the layman definition of entropy).

How do you find the entropy of a coin toss?

To calculate the entropy of 5 consecutive coin tosses, where each toss is independent of other tosses, we can sum the individual entropies for each coin toss. The result is H(X) = 5. So we can communicate the result of 5 coin tosses with just 5 bits, each bit representing the result of each coin toss.

How do you know if a coin is biased?

The solution can be derived using Bayes’ Theorem:

1. P(A|B)=P(B|A)P(A)P(B)
2. You want to know the probability of P(biased coin|three heads).
3. With a fair coin, the probability of three heads is 0.53=1/8.
4. The probability of picking the biased coin: P(biased coin)=1/100.