A dealer has just observed a buy order and updated the poste

A dealer has just observed a buy order and updated the posterior probability that value is high to 0.70 (value high = 102, low = 98). A second buy order then arrives. In this model informed traders buy when value is high with probability 0.9 and when value is low with probability 0.1 (noise component already folded in). Treating the post-first-trade posterior as the new prior, what is the posterior P(high) after the second buy, and the new fair value?