Probability Question 230
Question: Let S be a set containing n elements and we select 2 subsets A and B of S at random then the probability that $ A\cup B=S $ and $ A\cap B=\varphi $ is
[Orissa JEE 2005]
Options:
A) $ 2^{n} $
B) $ n^{2} $
C) 1/n
D) $ 1/2^{n} $
Show Answer
Answer:
Correct Answer: D
Solution:
Ways of selection two subset of $ A={{(2^{n})}^{2}} $ Ways of selection $ A\cup B $ and $ A\cap B $ are $ 2^{n} $
Required probability $ =\frac{\text{favourable cases}}{\text{total cases}}=\frac{2^{n}}{{{(2^{n})}^{2}}}=\frac{1}{2^{n}} $ .
BETA
