# hw2 - STAT 350 Spring 2009 Homework#2 Solution covers...

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STAT 350 – Spring 2009 Homework #2 Solution covers through Lecture C Text Exercises Chapter 5, Problems #2, 18, 20 Hint 5.2(f): the question does not specify whether Plant #3 is completed on time or not. 5.2 (a) At least one of the plants is completed on time: E 1 E 2 E 3 (b) All of the plants are completed on time E 1 E 2 E 3 (c) None of the plants are completed on time E 1 ' E 2 ' E 3 ' (d) Only Plant 1 is completed on time E 1 E 2 ' E 3 ' (e) Exactly one of the plants is completed on time (E 1 E 2 ' E 3 ') (E 1 ' E 2 E 3 ') (E 1 ' E 2 ' E 3 ) (f) Either Plant 1 or Plant 2 or both are completed on time: E 1 E 2 Homework #2 - Solution Page 1 of 6

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5.18 Let A 1 denote the event that person 1 has blood type A (etc.) a. P(A 1 and A 2 ) = P(A 1 )P(A 2 ) = (0.42)(0.42) = 0.1764 b. P(B 1 and B 2 ) = 0.10 2 = 0.01 P(AB 1 and AB 2 ) = 0.04 2 = 0.0016 P(O 1 and O 2 ) = 0.44 2 = 0.1936 c. P(two randomly chosen people have the same blood type) = P(A 1 and A 2 ) + P(B 1 and B 2 ) + P(AB 1 and AB 2 ) + P(O 1 and O 2 ) = 0.3816 d. This is the complement of the event in (c): Answer = 1 – 0.3816 = 0.6184 5.20 Let A = the event that the top subsystem works, B = the event the bottom subsystem works P(A) = P(1 works OR 2 works) = P(1 works) + P(2 works) – P(1 works and 2 works) = 0.9 + 0.9 – 0.9 2 = 0.99 P(B) = P(3 works AND 4 works) = 0.9 2 = 0.81 P(system works) = P(A OR B) = P(A) + P(B) – P(A and B) = P(A) + P(B) – P(A)P(B) = 0.99 + 0.81 – (0.99)(0.81) = 0.9981 Then answer the following problems: 1. A jar contains 25 balls, numbered 1 to 25. A ball is randomly selected from this jar Let A be the set of odd numbers Let B be the set of numbers less than 15 Let C be the set of multiples of 3 a. Give the members of the set B (A C) Numbers that are less than 20 OR are odd multiples of 3
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hw2 - STAT 350 Spring 2009 Homework#2 Solution covers...

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