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Suppose P ( A B c C ) = 0 . 65 , P ( A C ) = 0 . 2 , P ( A c B ) = 0 . 25

P ( A c C c ) = 0 . 25 , P ( B C c ) = 0 . 30 . Determine P ( A C c A c C ) B c .

Then determine P ( A B c A c ) C c and P ( A c ( B C c ) ) , if possible.

% file npr02_06.m % Data file % Data for [link] minvec3 DV = [A|Ac; A|(Bc&C); A&C; Ac&B; Ac&Cc; B&Cc];DP = [1 0.65 0.20 0.25 0.25 0.30];TV = [((A&Cc)|(Ac&C))&Bc; ((A&Bc)|Ac)&Cc; Ac&(B|Cc)];disp('Call for mincalc') npr02_06 % Call for dataVariables are A, B, C, Ac, Bc, Cc They may be renamed, if desired.Call for mincalc mincalcData vectors are linearly independentComputable target probabilities 1.0000 0.3000 % The first and third target probability3.0000 0.3500 % is calculated. Check with minterm map. The number of minterms is 8The number of available minterms is 4 Available minterm probabilities are in vector pmaTo view available minterm probabilities, call for PMA
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Suppose P ( A B c A c B ) C = 0 . 4 , P ( A B ) = 0 . 2 , P ( A c C c ) = 0 . 3 , P ( A ) = 0 . 6 , P ( C ) = 0 . 5 , and P ( A B c C c ) = 0 . 1 . Determine P ( A c C c A C ) , P ( A B c A c ) C c , and P ( A c ( B C c ) ) , if possible.

% file npr02_07.m % Data for [link] minvec3 DV = [A|Ac; ((A&Bc)|(Ac&B))&C; A&B; Ac&Cc; A; C; A&Bc&Cc];DP = [ 1 0.4 0.2 0.3 0.6 0.5 0.1];TV = [(Ac&Cc)|(A&C); ((A&Bc)|Ac)&Cc; Ac&(B|Cc)];disp('Call for mincalc') npr02_07 % Call for dataVariables are A, B, C, Ac, Bc, Cc They may be renamed, if desired.Call for mincalc mincalcData vectors are linearly independent Computable target probabilities1.0000 0.7000 % All target probabilities calculable 2.0000 0.4000 % even though not all minterms are available3.0000 0.4000 The number of minterms is 8The number of available minterms is 6 Available minterm probabilities are in vector pmaTo view available minterm probabilities, call for PMA
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Suppose P ( A ) = 0 . 6 , P ( C ) = 0 . 4 , P ( A C ) = 0 . 3 , P ( A c B ) = 0 . 2 ,

and P ( A c B c C c ) = 0 . 1 .

Determine P ( A B ) C c , P ( A C c A c C ) , and P ( A C c A c B ) , if possible.

% file npr02_08.m % Data for [link] minvec3 DV = [A|Ac; A; C; A&C; Ac&B; Ac&Bc&Cc];DP = [ 1 0.6 0.4 0.3 0.2 0.1];TV = [(A|B)&Cc; (A&Cc)|(Ac&C); (A&Cc)|(Ac&B)];disp('Call for mincalc')npr02_08 % Call for dataVariables are A, B, C, Ac, Bc, Cc They may be renamed, if desired.Call for mincalc mincalcData vectors are linearly independent Computable target probabilities1.0000 0.5000 % All target probabilities calculable 2.0000 0.4000 % even though not all minterms are available3.0000 0.5000 The number of minterms is 8The number of available minterms is 4 Available minterm probabilities are in vector pmaTo view available minterm probabilities, call for PMA
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Suppose P ( A ) = 0 . 5 , P ( A B ) = P ( A C ) = 0 . 3 , and P ( A B C c ) = 0 . 1 .

Determine P A ( B C c ) c and P ( A B A C B C ) .

Then repeat with additional data P ( A c B c C c ) = 0 . 1 and P ( A c B C ) = 0 . 05 .

% file npr02_09.m % Data for [link] minvec3 DV = [A|Ac; A; A&B; A&C; A&B&Cc];DP = [ 1 0.5 0.3 0.3 0.1];TV = [A&(~(B&Cc)); (A&B)|(A&C)|(B&C)];disp('Call for mincalc')% Modification for part 2 % DV = [DV; Ac&Bc&Cc; Ac&B&C];% DP = [DP 0.1 0.05];npr02_09 % Call for data Variables are A, B, C, Ac, Bc, CcThey may be renamed, if desired. Call for mincalcmincalc Data vectors are linearly independentComputable target probabilities 1.0000 0.4000 % Only the first target probability calculableThe number of minterms is 8 The number of available minterms is 4Available minterm probabilities are in vector pma To view available minterm probabilities, call for PMADV = [DV; Ac&Bc&Cc; Ac&B&C]; % Modification of dataDP = [DP 0.1 0.05];mincalc Data vectors are linearly independentComputable target probabilities 1.0000 0.4000 % Both target probabilities calculable2.0000 0.4500 % even though not all minterms are available The number of minterms is 8The number of available minterms is 6 Available minterm probabilities are in vector pmaTo view available minterm probabilities, call for PMA
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Source:  OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
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