Question 1186367
The prob'y that the 1st carton is rejected is {{{((matrix(2,1,2,2))*(matrix(2,1,10,1))+(matrix(2,1,2,1))*(matrix(2,1,10,2)))/((matrix(2,1,12,3))) = 5/11}}}.

The prob'y that the 2nd carton is rejected is {{{((matrix(2,1,1,1))*(matrix(2,1,11,2)))/((matrix(2,1,12,3))) = 1/4}}}.


Hence,

a)  Prob'y that carton 1 is rejected and carton 2 is accepted is {{{(5/11)*(3/4) =red(15/44)}}}.

b)  Prob'y that both cartons are accepted is {{{(6/11)*(3/4) =18/44 = red(9/22))}}}.

c)  Prob'y neither carton is accepted is {{{(5/11)*(1/4) = red(5/44))}}}.