1.

Let |X| dentoe the number of elements in a set X. Let S={1,2,3,4,5,6} be a sample space, where each element is equally likely to occur. If A and B are independent events associated with S, then the number of ordered paris , (A,B) such that 1le|B|lt|A|, equals............

Answer»


Solution :GIVEN sample space S `={1,2,3,4,5,6}` andlet there are `i` elements in set A an j elements in set B,
Now, according to information `1 le j lt I le 6`. So, total number of ways of choosing sets A and
`B=sum_(1lejltile6)(sum""sum) .^(6)C_(i)" ".^(6)C_(j)`
`=((UNDERSET(r=1)overset(6)(sum).^(6)C_(r))^(2)-underset(r=1)overset(6)(sum)(.^(6)C_(r))^(2))/(2)=((2^(6)-1)^(2)-(.^(12)C_(6)-1))/(2)`
`=((63)^(2)-(12!)/(6!6!)+1)/(2)`
`=(3969-924+1)/(2)=(3046)/(2)=1523`


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