Question: Basic Probability (2.5 points) Recall the game show Let's Make a Deal. You are a contestant and there is a fabulous prize behind door number

Basic Probability (2.5 points) Recall the game
Basic Probability (2.5 points) Recall the game show Let's Make a Deal. You are a contestant and there is a fabulous prize behind door number 1, door number 2, or door number 3. You have chosen door number 1. The host of the show opens door number 3 revealing a not-so-fabulous prize, and asks you if you want to change your mind. You have watched the show for a number of years and have noticed that the host always offers contestants the option of switching doors. Moreover, you know that when the host has a choice of doors to open (e.g. the prizes behind both doors 2 and 3 are duds), he chooses randomly. Should you switch to door 2 or stick with door 1 in order to maximize your chances of winning the fabulous prize? Find the following: i. Find the probability of winning the fabulous prize with the decision not to switch. (1.25 points) ii. Find the probability of winning the fabulous prize with the decision to switch. (1.25 points)

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