Question

Let the sample data be: w NWN NM wwNNN The conditional probability of C1 = 1 given 0 = 0, P (C1 = 1 0 = 0), is: 1/2 1/3 0114 - 0215

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Answer 1

Since,

P(A|B) = P(A and B) / P(B)

Total number of cases = 9

Total cases for which (c1 = 1 ) and (O = 0 ) are 2 and they are following

{(c1 = 1, c2 = 3, c3 = 1 , O = 0 ), (c1 = 1, c2 = 3, c3 = 3 , O = 0 )}

P( (c1 = 1 ) and (O = 0 )) = 2/9

Total cases for which (O = 0 ) are 2 and they are following

{(c1 = 1, c2 = 3, c3 = 1 , O = 0 ), (c1 = 1, c2 = 3, c3 = 3 , O = 0 ),(c1 = 3, c2 = 1, c3 = 2 , O = 0 ),(c1 = 2, c2 = 2, c3 = 1 , O = 0 )}

P(O = 0) = 4/9

P(( c1 = 1) | (O = 0 ) ) = P( (c1 = 1 ) and (O = 0 )) / P(O = 0) = ( 2/9 ) / ( 4/9 ) = 2 / 4 = 1/ 2

Answer is 1 / 2