Recitation 3 Solutions

# Recitation 3 Solutions - Steven Weber Dept of ECE Drexel...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2010) Recitation 3 Solutions Question 1 Recall the Monty Hall example from lecture. Please consider the following variants of the problem and compute the probabilities of winning by sticking and switching. Do any three of the four problems. 1. Suppose Monty does not now know the location of the car. After your initial choice, Monty opens one of the two remaining doors, selected at random. If his selected door reveals the car then you lose. If his selected door reveals a goat, then you get the option to stick with your original door or to switch to the remaining door. Define events: WS: win by switching IC: initial door is correct MC: Monty reveals the car Then the probability that you win by switching given that the initial choice is incorrect is: P ( WS | ¯ IC ) = P ( WS | ¯ IC, MC ) P ( MC | ¯ IC ) + P ( WS | ¯ IC, ¯ MC ) P ( ¯ MC | ¯ IC ) = 0 × 1 2 + 1 × 1 2 = 1 2 . (1) You can of course reason this out for yourself without formally applying this equation. This allows us to

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