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2.2 Problems on minterm analysis  (Page 3/6)

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Given: P ( A ) = 0 . 6 , P ( A c B c ) = 0 . 2 , P ( A C c ) = 0 . 4 , and P ( A C D c ) = 0 . 1 .

Determine P ( A c B ∪ A ( C c ∪ D ) ) .

% file npr02_10.m % Data for [link] minvec4 DV = [A|Ac; A; Ac&Bc; A&Cc; A&C&Dc];DP = [1 0.6 0.2 0.4 0.1];TV = [(Ac&B)|(A&(Cc|D))];disp('Call for mincalc') npr02_10Variables are A, B, C, D, Ac, Bc, Cc, Dc They may be renamed, if desired.Call for mincalc mincalcData vectors are linearly independent Computable target probabilities1.0000 0.7000 % Checks with minterm map solution The number of minterms is 16 The number of available minterms is 0Available minterm probabilities are in vector pma To view available minterm probabilities, call for PMA
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A survey of a represenative group of students yields the following information:

  • 52 percent are male
  • 85 percent live on campus
  • 78 percent are male or are active in intramural sports (or both)
  • 30 percent live on campus but are not active in sports
  • 32 percent are male, live on campus, and are active in sports
  • 8 percent are male and live off campus
  • 17 percent are male students inactive in sports

  1. What is the probability that a randomly chosen student is male and lives on campus?
  2. What is the probability of a male, on campus student who is not active in sports?
  3. What is the probability of a female student active in sports?
% file npr02_11.m % Data for [link] % A = male; B = on campus; C = active in sports minvec3DV = [A|Ac; A; B; A|C; B&Cc; A&B&C; A&Bc; A&Cc];DP = [ 1 0.52 0.85 0.78 0.30 0.32 0.08 0.17];TV = [A&B; A&B&Cc; Ac&C];disp('Call for mincalc')npr02_11 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 0.44002.0000 0.1200 3.0000 0.2600The number of minterms is 8 The number of available minterms is 8Available minterm probabilities are in vector pma To view available minterm probabilities, call for PMA
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A survey of 100 persons of voting age reveals that 60 are male, 30 of whom do not identify with a political party; 50 are members of a political party;20 nonmembers of a party voted in the last election, 10 of whom are female. How many nonmembers of a political party did not vote? Suggestion Express the numbers as a fraction, and treat as probabilities.

% file npr02_12.m % Data for [link] % A = male; B = party member; C = voted last election minvec3DV = [A|Ac; A; A&Bc; B; Bc&C; Ac&Bc&C];DP = [ 1 0.60 0.30 0.50 0.20 0.10];TV = [Bc&Cc];disp('Call for mincalc') npr02_12Variables 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 0.3000 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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During a period of unsettled weather, let A be the event of rain in Austin, B be the event of rain in Houston, and C be the event of rain in San Antonio. Suppose:

P ( A B ) = 0 . 35 , P ( A B c ) = 0 . 15 , P ( A C ) = 0 . 20 , P ( A B c ∪ A c B ) = 0 . 45
P ( B C ) = 0 . 30 P ( B c C ) = 0 . 05 P ( A c B c C c ) = 0 . 15
  1. What is the probability of rain in all three cities?
  2. What is the probability of rain in exactly two of the three cities?
  3. What is the probability of rain in exactly one of the cities?
% file npr02_13.m % Data for [link] % A = rain in Austin; B = rain in Houston;% C = rain in San Antonio minvec3DV = [A|Ac; A&B; A&Bc; A&C; (A&Bc)|(Ac&B); B&C; Bc&C; Ac&Bc&Cc];DP = [ 1 0.35 0.15 0.20 0.45 0.30 0.05 0.15];TV = [A&B&C; (A&B&Cc)|(A&Bc&C)|(Ac&B&C); (A&Bc&Cc)|(Ac&B&Cc)|(Ac&Bc&C)];disp('Call for mincalc') npr02_13Variables 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 0.2000 2.0000 0.25003.0000 0.4000 The number of minterms is 8The number of available minterms is 8 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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