Bayesian analysis of Price is Right showcase
Question
Suppose you're a contestant on a popular game show called the Price is Right. You've made it to 'The Showcase' round where you're tasked with guessing the price of a group of prizes (typically trips, cars, furniture, etc.). The rules for the round (simplified a bit for this question) are as follows:
 There are 2 contestants competing in a showcase round
 Both contestants are shown unique groups of prizes (2 groups of prizes shown in total)
 After seeing the prizes, each contestant is asked to bid on what they think the value is of their unique set of prizes
 Whichever bid is closer, without going over, wins. If a contestant bids over, then their bid is disqualified from winning
This game provides an interesting example of balancing uncertainty with risk (since if we bid even 1 dollar over the true price of the items we are disqualified).
Given this information, you're tasked with using Bayesian inference to build a model and select your final bid in the showcase. Below are some details for your specific showcase round (the exact #s are not important, but will be helpful for plugs/structuring your own bets):

You can assume that you have data on the 'true prices' of past Price is Right Showcase prizes, and they are normally distributed with a mean of 23,000 and a standard deviation of 4,500

The two prizes in your prize package for today are:

Trip to Hawaii

Set of living room furniture
Note that this is an example of a 'case study' type question that is pretty openended, so focus on structuring your process/logic more so than your actual numerical answer. At a high level we'll step through comparing our estimate for this specific prize package to the historical mean/standard deviation (using Baysian inference), and we'll then set up functions to quantify and account for risk before arriving at our final bid.