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

Question

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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inventgm · Accepted Answer

Total Number of possible subsets   :  2^5  -- (A number can occur or not occur in a subset -- 2 ways)
Possible subsets where 5 is not present   :  2^4 * 1 .
P =  2^4  /  2^5  = 1 / 2.

chetan2u · Answer

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

mdeep92 · Answer

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

mdacosta · Answer

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

AOBang · Answer

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}

majumdarnitw · Answer

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

MathRevolution · Answer

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

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