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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...
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 = 8Case 2 when the second of the pair contains all 3 elements, that is when it is equal to S, n = 6Case 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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