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One number, n, is selected at random from a set of 10 intege

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One number, n, is selected at random from a set of 10 intege [#permalink] New post 05 May 2013, 21:20
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One number, n, is selected at random from a set of 10 integers. What is the probability that ½ n + 13 = 0 ?

(1) The largest integer in the set is 13.
(2) The arithmetic mean of the set is zero.
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Re: One number, n, is selected at random from a set of 10 intege [#permalink] New post 05 May 2013, 21:52
Both statements seem quite ambiguous considering that we are dealing with a set of random integers. We essentially need the probability of N = 26
Statement 1 : there may be any number of integers less than 13 the set could consist of 9, -26's and one 13 or one -26, 13 and eight other integers
Statement 2 : The set could have any 5 negative numbers and the same numbers in positive as well making the average 0. The statement can in no way specify exactly how many times -26 appears in the set.

Both statements taken together also cannot conclusively give the no. of times -26 appears in the set. If -26 appears once in the set it could be offset in the average by 13, 12 & 1. 2 nos. of 26 similarly could be offst in the average by 13,12,11,10,6.

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Last edited by aceacharya on 05 May 2013, 22:02, edited 1 time in total.
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Re: One number, n, is selected at random from a set of 10 intege [#permalink] New post 05 May 2013, 21:53
Expert's post
rajatr wrote:
One number, n, is selected at random from a set of 10 integers. What is the probability that ½ n + 13 = 0 ?

1 .The largest integer in the set is 13.
2. The arithmetic mean of the set is zero.


For n/2+13 = 0, n = -26.

From F.S 1, we have the largest integer as 13. Thus the set could have all 10 positive integers including 13 in which case the probability - 0. Also, the number -26 could be included in some other combinations of 10 integers, where the probability would be a non-zero entity. Insufficient.

From F.S 2, as the arithmetic mean of the set is zero, hence the sum of all the ten integers is zero. Again, the presence/absence of -26 is not ascertained from this fact statement.Insufficient.

Combining both, for set -26,-5,-3,-2,0,2,4,8,9,13 --> the probability is 1/10

Again, for the set -13,-4,-3,-2,-1,1,2,3,4,13 --> the probability is 0. Insufficient.

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Re: One number, n, is selected at random from a set of 10 intege   [#permalink] 05 May 2013, 21:53
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