Given a set x with n elements, and sets a and b which are subsets of x, what is the probability of a being a subset of b?
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(3/4)^N this the right answer.
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Given,
A set x id=s given with the n elements.
The set a and b are subsets of x.
To find,
We have to find the probability of a being the subset of b.
Solution,
The required probability of a being the subset of b is (3/4)^N.
It is given that x is the set with n elements i.e.
x = { a1,a2,----,an)
We have a total number of four cases
⇒ ai ∈ a and ai ∈ b
⇒ai ∉ a and ai ∈ b
⇒ai ∉ a and ai ∉ b
⇒ ai ∉ a and ai ∉ b
Total number of ways = 4^n
Favorable cases = 3^n
Probability = (3/4)^n
Hence, the required probability is (3/4)^n.
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