In Laplace’s rule of succession (Example 5e), suppose that

Step 1 of 2

(a)

We are asked to find the probability that the  flip turns up heads is

To do so, you will have to prove and use the identity

Integrating by parts yields

In Laplace’s rule of succession, we assume we have  coins, the  one of which yields heads when flipped with probability

First,  flips of the chosen coin result in  heads and  tails.

Let  denote the event that the  flip will land heads.

Then conditioning on the chosen coin  for  we have the following

Using Bayes’ rule