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There is a set consisting of 5 numbers--{1,2,3,4,5}.

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chetan2u
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There is a set consisting of 5 numbers--{1,2,3,4,5}. [#permalink] New post   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



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D
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Re: There is a set consisting of 5 numbers--{1,2,3,4,5}. [#permalink] New post   05 Apr 2016, 20:46
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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


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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}. [#permalink] New post   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}. [#permalink] New post   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}. [#permalink] New post   08 May 2016, 19:49
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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



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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 =\(2^5-2^4 = 2^4(2-1) = 2^4\)...
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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There is a set consisting of 5 numbers--{1,2,3,4,5}. [#permalink] New post   14 Jul 2019, 01:47
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Here comes the concept of POWER SET.
POWER SET - Set of all subset of A ( where A is any set) is a POWER SET.
Let Set A has n elements.
So Power Set will have - \(2^n\) elements

Now , Total number of subset of A will be \(2^5\) = 32
This 32 will be total cases
In question we want all possible sets in which 5 is not the largest number.
As in A = {1,2,3,4,5} , 5 is greatest so we will exclude 5
So now all subset of Set A' {1,2,3,4} will be our favorable cases i.e. \(2^4\) = 16

So required probability = \(\frac{favorable.cases}{total.cases}\) = \(\frac{16}{32}\) = \(\frac{1}{2}\)

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Re: There is a set consisting of 5 numbers--{1,2,3,4,5}. [#permalink] New post   06 Aug 2020, 01:20
Let Set X = ( 1,2,3,4,5)

No. of subsets of X >>N1 = 2^ n(X) = 2^5

Set w/o element "5" Y = (1,2,3,4)
No. of Subsets of Y>>>N2 = 2^n(Y) = 2^4

So, Probability of selecting subsets w/o "5" = N2/N1 = 2^4/2^5 = 1/2
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Re: There is a set consisting of 5 numbers--{1,2,3,4,5}. [#permalink] New post   06 Aug 2020, 03:17
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Given set : {1,2,3,4,5}

Number of elements: 5
Number of subset: 2 ^5 = 32 (Null set included) - Total outcomes

Given condition: '5' is to be excluded in all possible selected subset: Hence,

The number of elements remains 4.
Number of subset: 2 ^4 = 16 (Null set included) - Desired outcomes

Probability = \(\frac{Desired Outcomes}{Total outcomes}\) = \(\frac{16}{32}\) = \(\frac{1}{2}\)

Answer: D
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Re: There is a set consisting of 5 numbers--{1,2,3,4,5}. [#permalink]
06 Aug 2020, 03:17
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