# Answer each of the following truefalse questions a it

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Answer each of the following True/False questions. a) It is possible for ( ) 0 P E b) It is possible for ( ) 1 P E c) It is possible for ( ) 1.1 P E d) It is possible for ( ) .2 P E  e) If 1 ( ) .7 P E and 2 ( ) .5 P E , it is possible for 1 E to be a subset of 2 E . f) If 1 ( ) .7 P E and 2 ( ) .5 P E , it is possible for 2 E to be a subset of 1 E . g) If 1 ( ) .7 P E and 2 ( ) .5 P E , it is possible for 1 E and 2 E to be disjoint. h) If 1 ( ) .5 P E and 2 ( ) .5 P E , it is possible for 1 E and 2 E to be disjoint. 13. For each functions P below. Determine the value of c that makes the column a probability function. 14. Suppose that our sample space for our experiment is 1 2 3 s , s , s , 1, 2, 3, S . a) Is 1 ( ) 1 P n n a plausible probability function for our sample space? b) Determine the value of p , so that n P n p is a legal probability function on our sample space. Section 2.4 Rules of Probability 15. Use the accompanying diagram to determine the probabilities: a) ()CP Bb) ( )P Ac) ()P ABCd) []P ACe) []P ABf) []P CAg) []P CBh) [() ]CP ABi) []P CBA j) C C P B k) [( ) ] C P A B C l) [ ] P A B s P 1 (s) P 2 (s) P 3 (s) P 4 (s) P 5 (s) P 6 (s) P 7 (s) 1 .2 .1 .2 c 1/8 .1 .15 2 .2 .1 .1 .1 1/7 .1 .1 3 c c -.1 .2 1/6 .2 .1 4 .2 .1 .2 .1 1/5 .2 .1 5 .2 .1 c .2 1/4 .25 c 6 .2 .1 .3 .5 c 4c .85 - 2c
m) [ ( ] P A B C n) [(]P ABC 16. Two events, A and B, are such that ( ) .45, ( ) .65, ( ) .25 P A P B P A B , determine ( ) P A B . 17. Two events, A and B, are such that ( ) .45, ( ) .65, ( ) .7 P A P B P A B , determine ( ) P A B . 18. Two events, A and B, are such that ( ) .45, ( ) .65, ( ) .25 P A P B P A B , determine ( ) C P B A . 19. Two events, A and B, are such that ( ) .45, ( ) .35, ( ) .6 P A P A B P A B , determine ( ) P B . Section 2.5 Probability as Relative Frequency 20. Suppose that we asked 2000 people what their blood type is (O, A, B or AB) and what ethnic group they belong to (G1, G2 or G3). The results of the survey are listed in the table below. Blood Type Total Ethnic Group O A B AB G1 300 150 175 25 650 G2 125 650 15 10 800 G3 165 145 175 65 550 Total 590 945 365 100 2000 The numbers in the center of the table are the number of the people in the survey that answered the ethnic question as stated in that row and answered the blood type question as stated in that column. For example, 300 people have type O blood and are in group G1. The totals are in the outer row and column of the table. The total of 2000 can be determined by summing up the row totals or summing up the column totals. Determine the following probabilities. a) ( 1) P G b) ( ) P A c) ( ) P A B d) [ 2] P A G e) [ 1 2] P G G f) [ 3 ) P G O g) [ 3 ] P G O h) [ 1 2 ] P G G AB i) [( 1 2) ] P G G AB j) ( ) C P B k) [( 3) ] C P A G l) [( 2 ) ] C P G AB
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