Question

Q2. Bayesian Rule and Conditional Probability (50 points): You are hosting a group of friends for your Birthday party today and as you wake up early in the morming to start preparing the food, the sky is cloudy. In general, 50% of all rainy days start cloudy, but cloudy mornings are common (about 40% of the days start cloudy. This is usually a dry month (which means typically only 10% of the days tend to be rainy). If this cloudy morning turns out to be a rainy day, there's a 50% chance that not all your friends can make it to your party. You think of 3 options for food, first, do a barbeque in your backyard, second, invite your friends to your favorite restaurant, or cook in your kitchen. Here are some details about the price values for the 3 options you have: Cooking indoors: this option costs you $190. Going to a restaurant: if it does not rain, all your invited friends will show up and you expect to spend about $ 300, if it rains and not all your friends show up (about 70% show up) you will be spending $ 200 and if they all show up despite rain, you will again be spend $ 300. Barbeque: you are going to get barbeque stuff for $ 180 and if it does not rain, that is your total expense, but if it rains, you have no other choice other than changing your plan to a restaurant at the last minute and the expenses at the restaurant would be the same in case all or part of your friends show up. Set a precision tree for this problem and decide on which option results in a lower cost value.

Answer 1

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