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Problem1-Solutions

Problem1-Solutions - 1 Assignment 1 STAT220-Fall 2010...

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1 Assignment 1, STAT220-Fall 2010 Instructor: Kamyar Moshksar Due on September 20th Problem 1 - Fig. 1 demonstrates the blocks in the downtown of a city. There are a total of 60 blocks. A cab driver starts at point A and is called to go to point B. What is the probability that it passes by intersection C shown in the figure. It is assumed that the cab driver only goes towards north or east at each intersection with a probability of 0 . 5 each. B NORTH EAST WEST SOUTH C A Fig. 1. Solution: In order to go from A to B, the cab driver must take 6 steps towards east (E) and 10 steps towards north (N). Therefore, the number of ways he can do the trip is the same thing as arranging 6 letters E and 10 letters N on a line which is 16! 6!10! . By the same token, there are 4! 1!3! ways to travel from A to C and 12! 5!7! ways to travel from C to B. Hence, the answer is 4! 1!3! 12! 5!7! 16! 6!10! . Problem 2- A box contains n balls numbered 1 through n . Suppose k balls are drawn in succession. (a)What is the probability that m is the largest number drawn? (b) what is the probability that the largest number drawn is less than or equal to m ?

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Problem1-Solutions - 1 Assignment 1 STAT220-Fall 2010...

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