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Let S be a set with 3 elements. What is the probabilty of choosing an ordered pair (A,B) of subsets of S such that A and B are disjoint? 1/2 27/64 26/64 1/8 Please explain the solution also...

Let S be a set with 3 elements. What is the probabilty of choosing an ordered pair (A,B) of subsets of S such that A and B are disjoint?
  1. 1/2
  2. 27/64
  3. 26/64
  4. 1/8
Please explain the solution also...

Grade:12th pass

1 Answers

Ayush Anand
126 Points
10 months ago
Ans is 26/64.
For this we need to calculate cases when the elements of the ordered pair are common,and then subtract it from 1.
For sample space, the total number of subsets is 23 = 8.
Number of ordered pair = 8×8 = 64.
 
For calculating ordered pairs that have common elements, divide in 3 cases.
Case 1 when the ordered pairs are same, n = 8
Case 2 when the second of the pair contains all 3 elements, that is when it is equal to S, n = 6
Case 3 when the second of the pair contains any two elements, for each one n = 4. So for 3, n = 4×3 = 12.
Adding the above we get, 12+8+6 = 26.
 
So, the answer is 26/64.
 
I can't attach photo of the solution here so it is difficult to type the 3 cases taken when they are common. If it feels this is not clear please share a means to share the pic.

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