MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Civil and Environmental Engineering
1.017/1.010 Computing and Data Analysis for Environmental
Applications/Uncertainty in Engineering
Problem Set 2: Combinatorial Methods for Deriving Probabilities
Due: Thursday, September 25, 2003
Problem 1
This is a classic combinatorial probability problem that can be solved by applying the
counting and combinatorial principles from Lecture 4.
Suppose that three balls are
drawn successively and randomly from a box containing 6 red balls, 4 white balls, and 5
blue balls that are identical except for their colors.
Determine the probability that these
balls are drawn
in the order
red, white, blue if 1) each ball
is replaced
after it is drawn
2) each ball
is not replaced
after it is drawn.
Note that since order is important you need
to consider permutations rather than combinations when evaluating the number of
outcomes for each event.
Problem 2
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 Spring '05
 GeorgeKocur
 Combinatorics, Environmental Engineering, Probability theory, Enumerative combinatorics, Department of Civil and Environmental Engineering, combinatorial probability problem

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