We feel happy when web-browsing operations provide us with necessary information; otherwise, we feel bitter. How to measure this happiness (or bitterness)? How does the profile of happiness grow and decay during the course of web-browsing? We propose a probabilistic framework that models evolution of user satisfaction, on top of his/her continuous frustration at not finding the required information. It is found that the cumulative satisfaction profile of a web-searching individual can be modeled effectively as the sum of random number of random terms, where each term is mutually independent random variable, originating from 'memoryless' Poisson flow. Evolution of satisfaction over the entire time interval of user's browsing was modeled with auto-correlation analysis. A utilitarian marker, magnitude of greater than unity of which describe happy web-searching operations; and an empirical limit that connects user's satisfaction with his frustration level - are proposed too. Presence of pertinent information in the very first page of a web-site and magnitude of the decay parameter of user satisfaction (frustration, irritation etc.), are found to be two key aspects that dominate web-browser's psychology. The proposed model employed different combination of decay parameter, searching time and number of helpful web-sites. Obtained results are found to match the results from three real-life case-studies.