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HW2-soln

# HW2-soln - IE 111 Fall Semester 2007 Homework#2 Solutions...

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IE 111 Fall Semester 2007 Homework #2 Solutions Note: these are not necessarily in order from easy to hard. They should keep you busy, some are pretty tricky, have fun. Question 1. Three fair coins are tossed. Find the following: a) P(TTT) b) P(TTH) c) P(more heads than tails) d) P(more heads than tails | at least one tail) e) P(Exactly one head | at least two tails a) 1/8 b) 1/8 c) 4/8 d) TTT,TTH,THT,HTT,THH,HTH,HHT: 3/7 e) TTT,TTH,THT,HTT: ¾ Question 2. There are 4 men and 5 women at a meeting. a) How many ways are there to select a committee of 3 people? 9 C 3 b) How many ways are there to select a committee of 3 people if exactly one must be male? 4 C 1 * 5 C 2 c) How many ways are there to select a committee of 3 people if at least one must be male? 4 C 1 * 5 C 2 + 4 C 2 * 5 C 1 + 4 C 3 * 5 C 0 or equivalently 9 C 3 - 5 C 3 Question 3. There are 40 ping pong balls labeled from 1 to 40 in the pick-six lotto game. Six balls are picked randomly (without replacement) from the 40. What is the probability that the 6 numbers picked are the same as the six numbers you picked earlier in the day? 1/( 40 C 6 )

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Question 4. a) For a nine person baseball team, how many different batting orders are there? 9! b) A bar sells 12 varieties of domestic beer and 8 varieties of imported beer. How many ways are there to select 3 (different) domestic and 4 (different) imported brands? ( 12 C 3 )( 8 C 4 ) c) An urn contains 5 blue, 6 red, and 7 black marbles. You draw 4 marbles without replacement. Given that you got no blue marbles, what is the probability that you got exactly 2 red marbles? ( 6
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HW2-soln - IE 111 Fall Semester 2007 Homework#2 Solutions...

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