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In fact, recall Example 5 dealing with the contaminated corn crop. What are all the possibilities
for shipping out two bushels from the total of 20 Let‟s list them out:
0 contaminated bushels and 2 uncontaminated bushels ship (call it
) )
1 contaminated and 1 uncontaminated bushels ship (call it )
2 contaminated bushels ship (call it )
Are there any others Not unless there is a possibility we have not considered. Since two bushels
are guaranteed to go out, the outcome must fall into one of the three categories listed.
Let‟s calculate the probability for each of these by hand:
( ) ( )
( ) ( )
( ): there are two possibilities; either the first is contaminated and the second is not, or
vice versa. We must consider both outcomes below:
o ( )
( ) ( )
o ( )
( ) ( )
These two possibilities give 9.5% + 9.5% = 19% of the sample space.
( ) (from previous calculation)
(NOTE: Importantly, summing these three probabilities gives 1, as stated in the axioms!)
Statistics for Decision-Making in Business © Milos Podmanik Page 94