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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 1/8Please explain the solution also...

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.