CBSE Class 12-science Answered

Two integers are selected at random from integers 1 through 11. If the sum is even, find the probability that both the numbers are odd.

Asked by Topperlearning User | 19 Aug, 2016, 05:05: PM

Expert Answer

$O u t space o f space t h e space 11 space i n t e g e r s space 5 space a r e space e v e n space a n d space 6 space a r e space o d d A equals b o t h space n u m b e r s space a r e space o d d B equals s u m space o f space n u m b e r space c h o s e n space i s space e v e n f r o m space o d d space i n t e g e r s left parenthesis 1 comma 3 comma 5 comma 7 comma 9 comma 11 right parenthesis space 2 space i n t e g e r s space c a n space b e space c h o s e n space i n space C presuperscript 6 subscript 2 space w a y s F o r space t h e space s u m space t o space b e space e v e n space t h e space 2 space i n t e g e r s space c a n space e i t h e r space b e space e v e n space o r space b e space o d d space s o space 2 space n u m b e r s space w h o s e space s u m space w i l l space b e space e v e n space c a n space b e space c h o s e n space i n space C presuperscript 6 subscript 2 plus C presuperscript 5 subscript 2 space w a y s P left parenthesis A right parenthesis equals fraction numerator C presuperscript 6 subscript 2 over denominator 11 C subscript 2 end fraction space a n d space P left parenthesis B right parenthesis equals fraction numerator C presuperscript 6 subscript 2 plus C presuperscript 5 subscript 2 over denominator C presuperscript 11 subscript 2 end fraction space P left parenthesis A intersection B right parenthesis equals fraction numerator C presuperscript 6 subscript 2 over denominator C presuperscript 11 subscript 2 end fraction T H E space R E Q U I R E D space P R O B A B I L I T Y equals P left parenthesis A divided by B right parenthesis equals fraction numerator P left parenthesis A intersection B right parenthesis over denominator P left parenthesis B right parenthesis end fraction equals fraction numerator C presuperscript 6 subscript 2 over denominator C presuperscript 6 subscript 2 plus C presuperscript 5 subscript 2 end fraction equals 3 over 5$