One third of the students in a class are ggirls and the rest are boys. The probability that a ggirl gets a first class is 0.4 and that of a boy is 0.3. If a student having first class is selected, find the probability that the student is a ggirl.

Asked by deepanshi bansal | 5th Nov, 2014, 07:52: PM

Expert Answer:

L e t space E subscript 1 comma E subscript 2 space a n d space A thin space b e space t h e space e v e n t s. E subscript 1 equals E v e n t space t h a t space a space b o y space i s space s e l e c t e d E subscript 2 equals E v e n t space t h a t space a space g i r l space i s space s e l e c t e d A equals E v e n t space t h a t space s t u d e n t space i s space h a v i n g space f i r s t space c l a s s L e t space t h e space n u m b e r space o f space s t u d e n t s space i n space a space c l a s s space b e space x. P left parenthesis E subscript 1 right parenthesis equals fraction numerator 2 x over denominator 3 end fraction P left parenthesis E subscript 2 right parenthesis equals x over 3 P open parentheses bevelled A over E subscript 1 close parentheses equals 0.3 P open parentheses bevelled A over E subscript 2 close parentheses equals 0.4 P open parentheses bevelled E subscript 2 over A close parentheses equals fraction numerator P left parenthesis E subscript 2 right parenthesis. P open parentheses bevelled A over E subscript 2 close parentheses over denominator P left parenthesis E subscript 1 right parenthesis. P open parentheses bevelled A over E subscript 1 close parentheses plus P left parenthesis E subscript 2 right parenthesis. P open parentheses bevelled A over E subscript 2 close parentheses end fraction equals fraction numerator begin display style x over 3 cross times 0.4 end style over denominator fraction numerator 2 x over denominator 3 end fraction cross times 0.3 plus x over 3 cross times 0.4 end fraction equals fraction numerator begin display style fraction numerator 0.4 over denominator 3 end fraction end style over denominator begin display style fraction numerator 0.6 over denominator 3 end fraction plus fraction numerator 0.4 over denominator 3 end fraction end style end fraction equals fraction numerator begin display style 0.4 end style over denominator begin display style 1 end style end fraction equals 0.4 P r o a b i b i l i t y space t h a t space a space f i r s t space c l a s s space s t u d e n t space s e l e c t e d space i s space a space g i r l space equals space 0.4

Answered by Prasenjit Paul | 6th Nov, 2014, 09:34: AM