Question

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?

Answer 1

Answer:

(3/4)^N this the right answer.

Answer 2

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.