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olganol [36]
3 years ago
7

Let ? = {a, b, c} be a sample space. let m(a) = 1/2, m(b) = 1/3, and m(c) = 1/6. find the probabilities for all eight subsets of

?.
Mathematics
1 answer:
Leviafan [203]3 years ago
5 0
<span>
A= {a,b,c} . Since this set has 3 elements, the number
of its total subset is 2³ = 8 (including the Ф element):

Here below all the subsets of {a,b,c}, with their related probabilities, knowing that P(a) = 1/2 ; P(b) = 1/3 and P(c) = 1/6

{a}        </span>→→→→1/2
<span>{b}        </span>→→→→1/3
<span>{c}        </span>→→→→1/6
<span>{a,b}     </span>→→→→1/2 + 1/3 =  5/6
<span>{a,c}     </span>→→→→1/2 + 1/6  =  2/3
<span>{b,c}     </span>→→→→1/3 + 1/6  =  1/2
<span>{a,b,c}  </span>→→→→1/2 + 1/3 + 1/6 = 1
<span>{∅}       </span>→→→→0 =0
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