Following information are given, 1. We start by assuming that the only thing that impacts the price setting behavior of the specialist is information. 2. There are two types of trader: informed (I) and liquidity or noise type of trader (N). The specialist worries that he may be trading against a trader of type I. We assume an equal probability of trading against I or N. 3. Assume the specialist is trading an asset of value A. This asset (for simplicity) may take a high value of H=1 or a low value of L=0. This is probabilistic, and we get H with probability p, and L with (1-p). 4. The specialist can set his expected value of the asset once he knows p, but he does not know this. He can only infer it from the trading behavior of others, and then synthesizes this information. What is the probability that Asset equals to H given that following trades are made

a. Sell, Sell, Buy, Buy

b. Sell, Sell, Sell, Sell

c. Sell, Sell, Buy, Sell, Buy