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July 30th, 2017, 03:28 AM   #1
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Puzzled by probability sample space

Question:
There are 2 blue pens (denoted as b1 and b2), 3 red pens (r1, r2, and r3), and 2 green pens (g1 and g2), in a closed box. Suppose you draw two pens together without first looking at the pens.

What is the sample space (given as a set.)

... Now the sample space is all the possible outcomes, what puzzles me here is do you consider the uniqueness of each pen when randomly drawing from the box?

Example:
S = {
(b1, b2), (b1, r1), (b1, r1), (b1, r2), (b1, r3), (b1, g1), (b1, g2),
(b2, r1), (b2, r1), (b2, r2), (b2, r3), (b2, g1), (b2, g2),
(r1, g1), (r1, g2), (r2, g1), (r2, g2), (r3, g1), (r3, g2)
}

Or am I just completely missing the point?
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July 30th, 2017, 05:04 AM   #2
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No, that is the point- of the sample space at least. You need to consider each individual pen or you are not taking into account the differing numbers of each kind of pen. You should have 20 such pairs but you do not because you do not have all possible pairings while you have several duplicates. For example you have (b1, r1) twice (in fact right next to each other) and you have (b2, r1) twice.

Do this: list b1 with all 6 other pens, then b2, then list r1 with all others except the blue pens, etc.:
(b1, b2), (b1, b3), (b1, r1), (b1, r2), (b1, r3), (b1, g1), (b1, g2)
(b2, b3), (b2, r1), (b2, r2), (b2, r3), (b2, g1), (b2, g2)
(r1, r2), (r1, r3), (r1, g1), (r1, g2)
(r2, r3), (r2, g1), (r2, g2)
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July 30th, 2017, 05:13 AM   #3
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Thanks Country Boy,

Completely missed those but happy to see I was heading in the right direction! Appreciate the help.
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August 14th, 2017, 09:44 AM   #4
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Haha, this was from the unisa assignment?
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August 14th, 2017, 09:46 AM   #5
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Distance learning isn't terribly fun when you confuse yourself by overthinking a problem.

Good to know you're on track with a solution.
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August 14th, 2017, 10:06 AM   #6
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Yeah I know the feeling... well good luck with this one, the final assignment before the exam! Hopefully we get the results soon...

I actually just joined the site because I believe to have found an issue with a probability question in assignment 6.... small world!
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