HW 2 Solutions

# HW 2 Solutions - Steven Weber Dept of ECE Drexel University...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2010) Homework 2 Solutions Question 1: Exercise 30, § 2.3, p65. A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet, all from diﬀerent wineries. If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? Order is important means we want a permutation. Use the permutation rule with n = 8 and k = 3. 8 × 7 × 6 = 336 . (1) If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to do this? If order is unimportant then we want a combination: ( 30 6 ) = 593 , 775. If order is important then we want a permutation: 30 × 29 × 28 × 27 × 26 × 25 = 427 , 518 , 000. If 6 bottles are to be randomly selected, how many ways are there to obtain two bottles of each variety? Use the product rule for k -tuples, here k = 3 is the number of types of wine: ( 8 2 )( 10 2 )( 12 2 ) = 83 , 160. If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? Use the fraction of combinations satisfying the criterion: P (two bottles of each variety in a randomly selected six) = ( 8 2 )( 10 2 )( 12 2 ) ( 30 6 ) = 0 . 140053 . (2) If 6 bottles are randomly selected, what is the probability that all of them are the same variety? The last question asked for an “and”, and required multiplication; this question asks for an “or”, and requires

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## This note was uploaded on 06/10/2010 for the course ENGR 361 taught by Professor Eisenstein during the Spring '04 term at Drexel.

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HW 2 Solutions - Steven Weber Dept of ECE Drexel University...

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