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Homework 2 - University of California San Diego ECE 109...

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University of California, San Diego ECE 109: Problem Set #2 1. Find in each of the following four cases: (a) , , and are disjoint events and . (b) (c) , , and (d) 2. Two fair dice are rolled. What is the conditional probability that the two dice show the same number given that the sum of the two numbers is greater than seven? 3. Let and be events. Show that . When does equality hold? 4. Monty Hall, the host of the TV game show “Let’s Make A Deal”, shows you three curtains. One curtain conceals a valuable prize, while the other two conceal junk. All three curtains are equally likely to conceal the prize. He offers you the following “deal”: pick a curtain, and you can have whatever is behind it. When you pick a curtain, instead of giving you what lies behind the curtain, Monty (who knows where the prize is) opens one of the remaining curtains to show you that there is junk behind it, and offers the following “new, improved deal”: you can either stick with your original choice, or switch to the remaining (unopened) curtain. Amidst the deafening roars of
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