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March 24th, 2013, 02:44 PM   #1
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help with probability please

B and R are members of a 15-person club that selects a president and
his assistant by lottery. What is the probability that B will be a president and R his assistant? (one person cannot hold 2 positions)
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March 24th, 2013, 05:08 PM   #2
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Re: help with probability please

2/15 * 1/14 (if 2 names drawn)
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March 24th, 2013, 05:17 PM   #3
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Re: help with probability please

Why 2/15?
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March 24th, 2013, 05:32 PM   #4
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Re: help with probability please

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Originally Posted by greg1313
Why 2/15?
1st draw: B or R (2 out of 15)
2nd draw (if 1st B or R): 14 left; so 1/14
Thassa way I read the problem...order does not count? No?
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March 24th, 2013, 05:37 PM   #5
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Re: help with probability please

Draw for president: 1/15. Then draw for assistant: 1/14. 1/15 * 1/14 = 1/210.
Draw for assistant: 1/15. Then draw for president: 1/14. 1/15 * 1/14 = 1/210.
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March 24th, 2013, 06:11 PM   #6
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Re: help with probability please

Yes, order does not count, so I figured I'd use the formula for permutations: Pn,r= n!/(n-r)! vs Cn,r=n!/r!(n-r)! (which is for problems where order doesn't matter)
I know that probability is counted as follows: P(E)= n(E)/n(S); in this case n(E) is number of elements in a compound event that can be broken down into two:
first, we choose B as the president P (given 15, choose 1) or, in other words, P15,1= 15!/14!=15
second, we choose R as assistant out of 14, since B is already a president: P (given 14, choose 1) or P14,1=14
Using multiplication principle we find out all the possible combinations: 14x15=210
Now, to calculate the probability, we need to divide the number of elements in the compound even (210) by the sample space (S) which is the list of all possible combinations... Isn't the sample space P15,2 (given 15, choose 2)??? So I divided 210 by 210 and got 1 which is unrealistic given the conditions of the problem... Where's my mistake?
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March 24th, 2013, 06:16 PM   #7
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Re: help with probability please

***Oops, my bad, it's the other way around. Here order matters because B must be the president and R his assistant, so I used the P formula as opposed to the C formula for where order does not matter.
Anyway, where's the mistake?
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March 24th, 2013, 07:51 PM   #8
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Re: help with probability please

IF that's the case, then problem should be clear and state:
1st draw = president, 2nd draw = assistant.

The way it reads now is:
2 names are drawn; if they're B and R, then B will be president and R the assistant.
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March 24th, 2013, 10:46 PM   #9
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Re: help with probability please

Well, the problem reads exactly as follows:
"Brittani and Ramon are members of a 15-person ski club. If a president and assistant selected by lottery, what is the probability that Brittani will be president and Ramon will be assistant? ( A person cannot hold more than one office)"
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