This paper is a brief analysis of the trading and pricing dynamics for a binary prediction market. This market is based on a constant product market maker. An AMM here serves a similar purpose as it does in a decentralized exchange like Uniswap. Liquidity providers collect a share of fees proportional to their contribution in return for providing liquidity to the market. The AMM here has 2 tokens representing the 2 outcomes of the prediction market. Buying a particular token is a proxy for believing in the outcome represented by that particular token. The paper derives various intuitive facts about the expected behaviour of such a market with respect to probabilities for the outcomes, spot prices, effective prices & how the prices vary in different situations. Some unintutive facts also emerge, for instance, that the spot price of an opposing token does not change when buying a particular outcome token. The general design is based on prior work done by Gnosis.