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

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Math Expert
Joined: 02 Aug 2009
Posts: 7587
There is a set consisting of 5 numbers--{1,2,3,4,5}.  [#permalink]

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05 Apr 2016, 20:11
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57% (01:58) correct 43% (02:13) wrong based on 123 sessions

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

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05 Apr 2016, 20:46
2
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
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}.  [#permalink]

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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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Joined: 05 Dec 2015
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Re: There is a set consisting of 5 numbers--{1,2,3,4,5}.  [#permalink]

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08 May 2016, 18:28

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
Math Expert
Joined: 02 Aug 2009
Posts: 7587
Re: There is a set consisting of 5 numbers--{1,2,3,4,5}.  [#permalink]

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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

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

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21 Aug 2017, 11:30
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Re: There is a set consisting of 5 numbers--{1,2,3,4,5}.   [#permalink] 21 Aug 2017, 11:30
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