# 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 : Option 1) Option 2) Option 3) Option 4)

As learnt in

Probability of occurrence of an event -

Let S be the sample space then the probability of occurrence of an event E is denoted by P(E) and it is defined as

- wherein

Where n repeated experiment and E occurs r times.

Total number of subsets of set

Number of subsets with one element =

Number of subsets with two elements=

.

.

.

.

Number of subsets with ten elements=

A and B are taken from P(x) from  subsets, total ways =

Number of ways =

Probability =

Option 1)

This option is incorrect.

Option 2)

This option is incorrect.

Option 3)

This option is incorrect.

Option 4)

This option is correct.

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