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There is a set consisting of 5 numbers{1,2,3,4,5}.
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05 Apr 2016, 20:11
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There is a set consisting of 5 numbers{1,2,3,4,5}. If all possible subsets including null set are created and one subset is picked up, what is the probability that the subset does not have 5 as its largest number? A. 1/5 B. 1/4 C. 1/3 D. 1/2 E. 4/5 Self Made
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1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
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Re: There is a set consisting of 5 numbers{1,2,3,4,5}.
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05 Apr 2016, 20:46
chetan2u wrote: There is a set consisting of 5 numbers{1,2,3,4,5}. If all possible subsets including null set are created and one subset is picked up, what is the probability that the subset does not have 5 as its largest number? A. 1/5 B. 1/4 C. 1/3 D. 1/2 E. 4/5
OA in 1 day Self Made KUDOS for best and shortest method Total Number of possible subsets [ including Null Subset ] : \(2^5\)  (A number can occur or not occur in a subset  2 ways) Possible subsets where 5 is not present [will include null subset] : \(2^4 * 1\). P = \(2^4\) / \(2^5\) = 1 / 2.



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Re: There is a set consisting of 5 numbers{1,2,3,4,5}.
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05 Apr 2016, 20:54
number of subsets of a set with n elements = 2^n
Number of proper subsets ( including null ) = 2^ 5 = 32
Probability = Number of subsets for elements (1 to 4) / Total number of subsets
Probability = 2^4 / 32 = 1/2



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Re: There is a set consisting of 5 numbers{1,2,3,4,5}.
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08 May 2016, 18:28
Answer: D
Each element is either in the set, or out, so total number of sets is 2^5 = 32
Then, excluding the 5 (which will automatically be the largest if included) you have 2^4 = 16
So, probability 5 not included is 16/32 = 1/2



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Re: There is a set consisting of 5 numbers{1,2,3,4,5}.
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08 May 2016, 19:49
chetan2u wrote: There is a set consisting of 5 numbers{1,2,3,4,5}. If all possible subsets including null set are created and one subset is picked up, what is the probability that the subset does not have 5 as its largest number? A. 1/5 B. 1/4 C. 1/3 D. 1/2 E. 4/5
Self Made TWO ways 1) NUmber of subsets of 4 items  1,2,3 and 4 = 2^4.. and # of subsets with all 5 items = 2^5... # of subsets with 5 =\(2^52^4 = 2^4(21) = 2^4\)... so prob = \(\frac{2^4}{2^5}= \frac{1}{2}\) D 2) there are certain subsets say x which can be made with 4 items, if you add 5th item to each, the number of subset will DOUBLE .. thus half of subsets will contain 5 in it.. P = 1/2
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1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
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Re: There is a set consisting of 5 numbers{1,2,3,4,5}.
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21 Aug 2017, 11:30
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