Snaptalk is a cell phone app that allows users to share photos and text messages, which self-destruct after a limited time period. Snaptalk's valuation depends on a number of uncertain factors, including potential market size and competition. For simplicity, suppose the market size will be either Large or Small, where the probability of a Large market size is 0.25. Given a Large market, Facebook will develop its own competing app with 0.80 probability. However, with only a Small market size, Facebook will develop an app with 0.40 probability. If Facebook does not develop an app, then Google will make an acquisition offer to Snaptalk with probability 0.60 (given a Large market), or with probability 1/3 (given a Small market). Regardless of market size, if Facebook develops its own app, then Google will not make an offer to Snaptalk. Google's offer, if one is made, depends on the size of the market. With a Large market, Google's offer will be $5 billion; but with a Small Market, the offer will be $1.5 billion.

(a) Given that Facebook develops its own app, what is the probability the market size is Large? (b) Are the events "Large market size" and "Facebook develops app" independent? Why or why not? (c) What is the probability that Snaptalk receives an offer from Google?