CBSE Class 12-science Answered

In a school, 5% of the boys and 1% of the girls have an IQ of more than 125.70% of the students are boys. If a student is selected and an IQ of 125 more than 125, find the probalility that the student is girl.

Asked by shreehari wadawadagi | 24 Feb, 2015, 06:08: PM

Expert Answer

$L e t space E space b e space t h e space e v e n t space s u c h space t h a t space t h e space I Q space o f space t h e space s t u d e n t space i s space 125 space o r space m o r e space t h a n space 125 L e t space G space b e space t h e space e v e n t space s u c h space t h a t space t h e space s e l e c t e d space s t u d e n t space i s space a space g i r l L e t space B space b e space t h e space e v e n t space s u c h space t h a t space t h e space s e l e c t e d space s t u d e n t space i s space a space b o y T h e r e f o r e comma P r o b a b i l i t y space o f space s e l e c t i n g space a space b o y comma space P open parentheses B close parentheses equals 70 over 100 equals 0.7 P r o b a b i l i t y space o f space s e l e c t i n g space a space g i r l comma space P open parentheses G close parentheses equals 30 over 100 equals 0.3 P r o b a b i l i t y space o f space g e t t i n g space a n space I Q space m o r e space t h a n space 125 space s u c h space t h a t space h e space i s space a space b o y comma space P open parentheses E vertical line B close parentheses equals 5 over 100 P r o b a b i l i t y space o f space g e t t i n g space a n space I Q space m o r e space t h a n space 125 space s u c h space t h a t space s h e space i s space a space g i r l comma space P open parentheses E vertical line G close parentheses equals 1 over 100 W e space n e e d space t o space f i n d space t h e space p r o b a b i l i t y space t h a t space t h e space s t u d e n t space i s space a space g r i l space s u c h space t h a t space h e r space I Q space i s space m o r e space t h a t space 125 T h a t space i s space w e space n e e d space t o space f i n d space P open parentheses G vertical line E close parentheses. P open parentheses G vertical line E close parentheses equals fraction numerator P open parentheses E vertical line G close parentheses cross times space P open parentheses G close parentheses over denominator P open parentheses E vertical line B close parentheses cross times space P open parentheses B close parentheses plus P open parentheses E vertical line G close parentheses cross times space P open parentheses G close parentheses end fraction space space space space space space space space space space space space space equals fraction numerator 1 over 100 cross times space 30 over 100 over denominator 5 over 100 cross times space 70 over 100 plus 1 over 100 cross times space 30 over 100 end fraction space space space space space space space space space space space space space equals fraction numerator 30 over denominator 5 cross times 70 plus 1 cross times 30 end fraction space space space space space space space space space space space space space equals fraction numerator 30 over denominator 350 plus 30 end fraction space space space space space space space space space space space space space equals 30 over 380 space space space space space space space space space space space space space equals 3 over 38$