<< Chapter < Page Chapter >> Page >

A television station runs a telephone survey to determine how many persons in its primary viewing area have watched three recent special programs, which wecall a, b, and c. Of the 1000 persons surveyed, the results are:

221 have seen at least a; 209 have seen at least b; 112 have seen at least c; 197 have seen at least two of the programs; 45 have seen all three; 62 have seen at least a and c; the number having seen at least a and b is twice as large as the number who have seen at least b and c.

  • (a) How many have seen at least one special?
  • (b) How many have seen only one special program?
% file npr02_16.m % Data for [link] minvec3 DV = [A|Ac; A; B; C; (A&B)|(A&C)|(B&C); A&B&C; A&C; (A&B)-2*(B&C)];DP = [ 1 0.221 0.209 0.112 0.197 0.045 0.062 0];TV = [A|B|C; (A&Bc&Cc)|(Ac&B&Cc)|(Ac&Bc&C)];npr02_16 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 0.30002.0000 0.1030 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
Got questions? Get instant answers now!

An automobile safety inspection station found that in 1000 cars tested:

  • 100 needed wheel alignment, brake repair, and headlight adjustment
  • 325 needed at least two of these three items
  • 125 needed headlight and brake work
  • 550 needed at wheel alignment

  1. How many needed only wheel alignment?
  2. How many who do not need wheel alignment need one or none of the other items?
% file npr02_17.m % Data for [link] % A = alignment; B = brake work; C = headlight minvec3DV = [A|Ac; A&B&C; (A&B)|(A&C)|(B&C); B&C; A ];DP = [ 1 0.100 0.325 0.125 0.550];TV = [A&Bc&Cc; Ac&(~(B&C))];disp('Call for mincalc') npr02_17Variables 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 0.2500 2.0000 0.4250The number of minterms is 8 The number of available minterms is 3Available minterm probabilities are in vector pma To view available minterm probabilities, call for PMA
Got questions? Get instant answers now!

Suppose P A ( B C ) = 0 . 3 , P ( A c ) = 0 . 6 , and P ( A c B c C c ) = 0 . 1 .

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

Repeat the problem with the additional data P ( A c B C ) = 0 . 2 and P ( A c B ) = 0 . 3 .

% file npr02_18.m % Date for [link] minvec3 DV = [A|Ac; A&(B|C); Ac; Ac&Bc&Cc];DP = [ 1 0.3 0.6 0.1];TV = [B|C; (((A&B)|(Ac&Bc))&Cc)|(A&C); Ac&(B|Cc)];disp('Call for mincalc') % Modification% DV = [DV; Ac&B&C; Ac&B];% DP = [DP 0.2 0.3];npr02_18 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 0.80002.0000 0.4000 The number of minterms is 8The number of available minterms is 2 Available minterm probabilities are in vector pmaTo view available minterm probabilities, call for PMA DV = [DV; Ac&B&C; Ac&B]; % Modified dataDP = [DP 0.2 0.3];mincalc % New calculation Data vectors are linearly independentComputable target probabilities 1.0000 0.80002.0000 0.4000 3.0000 0.4000The number of minterms is 8 The number of available minterms is 5Available minterm probabilities are in vector pma To view available minterm probabilities, call for PMA
Got questions? Get instant answers now!

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Applied probability' conversation and receive update notifications?

Ask