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# hw3sol - EE 351K Probability and Random Processes...

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EE 351K Probability and Random Processes FALL 2010 Instructor: Haris Vikalo [email protected] Homework 3 Solutions Problem 1 There are three dice in a bag. One has one red face, another has two red faces, and the third has three red faces. One of the dice is drawn at random from the bag, each die having an equal chance of being drawn. The selected die is repeatedly rolled. 1. What is the probability that red comes up on the first roll? 2. Given that red comes up on the first roll, what is the conditional probability that red comes up on the second roll? 3. Given that red comes up on the first three rolls, what is the conditional probability that the selected die has red on three faces? Solution: Let E i be the event that the die with i red faces is drawn from the bag, for i = 1 , 2 , or 3. Let R j denote the event that red comes up on the j -th role of the die. 1. P ( R 1 ) = P ( R 1 | E 1 ) P ( E 1 ) + P ( R 1 | E 2 ) P ( E 2 ) + P ( R 1 | E 3 ) P ( E 3 ) = 1 6 1 3 + 2 6 1 3 + 3 6 1 3 = 1 3 2. We need to find P ( R 2 | R 1 ) . First, P ( R 1 R 2 ) = P ( R 1 R 2 | E 1 ) P ( E 1 ) + P ( R

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hw3sol - EE 351K Probability and Random Processes...

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