Set, Relation and FunctionEasy
Question
Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is :
Options
A.
B.
C.
D.
Solution
Total number of subsubsets of set X = 210 = 1024
number of subsets with one element = 10C1
Number of subsets with two elements = 10C2
:
:
Number of subsets with 10 elements = 10C10
A & B are taken from P(X) from 210 subsets so total ways = 210,210
Number of ways such that A and B have equal number of elements =
(10C0)2 + (10C1)2 + (10C2)2 + ...... + (10C10)2
= 20C10
Probability =
number of subsets with one element = 10C1
Number of subsets with two elements = 10C2
:
:
Number of subsets with 10 elements = 10C10
A & B are taken from P(X) from 210 subsets so total ways = 210,210
Number of ways such that A and B have equal number of elements =
(10C0)2 + (10C1)2 + (10C2)2 + ...... + (10C10)2
= 20C10
Probability =
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