Question

A coin may or may not have a bias. It is thought that the coin has a 10% bias toward heads. A student is tasked with flipping the coin a thousand times to test this. The results come back as 575 times heads and 425 times tails. Is the coin biased? What is the true bias of the coin using a Bayesian update technique?

Answer 1

To check weather the coin is baised or not there are two way of determining the most common way is that filp the coin at bunch of times and see what fraction head and tell.

Here in this scenario the student is flip the coin 1000 times from that the p(head)= 0.575 and p(tail)=0.425 it means that

The coin is not perfectly unbiased

Actually no any real coin is truly unbiased in that sense. one side is always slightly heavier than other side.this causes the biased coin away from the 50/50 ratio.

The given coin is little biased towards head.

Now, According to the Bayesian technique,

Now most coins are being to fair or unbiased,

ie they have same probability of landing head tail (0.5)

You can talk about bais in terms of only one of these probabilities.

Now, iam going to measure the bias as the probability with which it lands tail.

Bias= P(tail)

Thank you.