Homework 4 - 550.420 Introduction to Probability Fall 2011...

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550.420 Introduction to Probability Fall 2011 Homework 4 Due Thursday September 29 [1] (2 points) Two fair dice are tossed 6 times, independently. What is the probability that the 6 th sum is not a repetition of a previous sum? [2] (2 points) Suppose that three numbers are selected one by one, at random, and without replacement, from the set of integers {1,2,3,….,n}. What is the probability that the third number falls between the first two if the first number is smaller than the second? [3] (2 points) Because of a prisoner’s constant pleading, the king grants him this favor: He is given 2N balls, which differ from each other only in that half of them are green and half are red. The king instructs the prisoner to divide the balls between two identical urns. One of the urns will then be selected at random, and the prisoner will be asked to choose a ball at random from the urn chosen. If the ball turns out to be green, the prisoner will be set free immediately. Otherwise, the prisoner will have to serve the rest of his 30 year sentence.
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