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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:

Options

  1. A2 10 - 1 2 20
  2. B20 C 10 2 20
  3. C20 C 10 2 10
  4. D2 10 - 1 2 10

Correct answer

B. 20 C 10 2 20

Step-by-step solution

The power set of X will contain 2 10 elements where each element is subset of A in which 10 C 0 will contain 0 element. 10 C 1 will contain 1 element. 10 C 2 will contain 2 elements. ⋮ ⋮ 10 C 10 will contain 10 elements. So total numbers of ways in which we can select two sets with replacement is And favorable cases would be 10 C 0 ⋅ 10 C 0 + 10 C 1 . 10 C 1 +   … … + 10 C 10 . 10 C 10 = 20 C 10 Hence, Probability would be =   20 C 10 2 20

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