Home
Class 12
MATHS
A is a set containing n elements. A subs...

A is a set containing n elements. A subset P of A is chosen at random. The set A is reconstructed by replacing the elements of P. A subset Q is again chosen at random. The Probability that `P cap Q` contain just one element, is

A

`2^(2n)-.^(2n)C_(n)`

B

`2^(n)`

C

`2^(n)-1`

D

`3^(n)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `A={a_(1),a_(2),a_(3), . . .,a_(n)}`
(i) `a_(i) in P,a_(i) in Q`
(ii) `a_(i) in P, a _(1) cancel(in)Q`
(ii) `a_(i) cancel(in)P,a_(i) in Q`
(iv) `a_(i) cancel(in)P,a_(i)cancel(in)Q,` where `1 le I le n`
`because P cap Q=phi` [cases in favour 3 i.e., (ii), (iii),(iv)]
`therefore`Required number of ways`=3^(n)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen, the number of ways of choosing so that (P cup Q) is a proper subset of A, is

A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset of A is again chosen. Find the number of ways of choosing P and Q, so that (i) P capQ contains exactly r elements. (ii) PcapQ contains exactly 2 elements. (iii) P cap Q=phi

A is a set containing n elements. A subset P of A is chosen at random and the set A is reconstructed by replacing the random. Find the probability that Pcup Q contains exactly r elements with 1 le r le n .

Let X be a set containing n elements. Two subsets A and B of X are chosen at random, the probability that AuuB=X is

Let X be a set containing n elements. If two subsets A and B of X are picked at random, the probability that A and B have the same number of elements is

A set contains 2n+1 elements. The number of subsets of this set containing more than n elements :

Let A be a set containing 10 distinct elements,then the total number of distinct functions from A to A is

The number of elements of the power set of a set containing n elements is

A book contains 1000 pages. A page is chosen at random. Find the probability that the sum of the digits of the marked number on the page is equal to 9.

The numbers of proper subset of set A having n elements are…… .