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CBSE Class 12-science Answered

Two bags A and B contain 4 white , 3 black and 2 white, 2 black balls respectively. From Bag A , 2 balls are drawn at random and transfered to bag B. Then a ball is drawn from bag B and is found to be black. What is the probability that the balls transfered were 1 white and 1 black?
 
                                                                        OR
 
In an exam 10 questions of true/false type are asked. a student tosses a fair coin to determine his answer. If the coin shows head he answers true or he answers false. Find the probability that he answered atmost 7 questions correctly.
Asked by Jayesh Pradhyumna | 14 Feb, 2015, 13:50: PM
answered-by-expert Expert Answer
L e t space E subscript 1 space b e space t h e space e v e n t space t h a t space t h e space b a l l s space t r a n s f e r r e d space a r e space b l a c k. L e t space E subscript 2 space b e space t h e space e v e n t space t h a t space t h e space b a l l s space t r a n s f e r r e d space a r e space w h i t e. L e t space E subscript 3 space b e space t h e space e v e n t space t h a t space 1 space b a l l space t r a n s f e r r e d space i s space b l a c k space a n d space a n o t h e r space b a l l space t r a n s f e r r e d space i s space w h i t e. L e t space A space b e space t h e space e v e n t space t h a t space t h e space b a l l space d r a w n space i s space b l a c k. P left parenthesis E subscript 1 right parenthesis equals fraction numerator 3 C 2 over denominator 7 C 2 end fraction equals 3 over 21 P left parenthesis E subscript 2 right parenthesis equals fraction numerator 4 C 2 over denominator 7 C 2 end fraction equals 6 over 21 P left parenthesis E subscript 3 right parenthesis equals fraction numerator 3 C 1 cross times 4 C 1 over denominator 7 C 2 end fraction equals 12 over 21 P open parentheses A over E subscript 1 close parentheses equals 4 over 6 P open parentheses A over E subscript 2 close parentheses equals 2 over 6 P open parentheses A over E subscript 3 close parentheses equals 3 over 6 P open parentheses E subscript 3 over A close parentheses equals fraction numerator P left parenthesis E subscript 3 right parenthesis cross times P open parentheses A over E subscript 3 close parentheses over denominator P left parenthesis E subscript 3 right parenthesis cross times P open parentheses A over E subscript 1 close parentheses plus P left parenthesis E subscript 3 right parenthesis cross times P open parentheses A over E subscript 2 close parentheses plus P left parenthesis E subscript 3 right parenthesis cross times P open parentheses A over E subscript 3 close parentheses end fraction equals fraction numerator 12 over 21 cross times 3 over 6 over denominator 3 over 21 cross times 4 over 6 plus 6 over 21 cross times 2 over 6 plus 12 over 21 cross times 3 over 6 end fraction equals fraction numerator 36 over 126 over denominator 12 over 126 plus 12 over 126 plus 36 over 126 end fraction equals 36 over 60 equals 3 over 5 P r o b a b i l i t y space t h a t space t h e space b a l l s space t r a n s f e r r e d space w e r e space 1 space w h i t e space a n d space 1 space b l a c k space equals 3 over 5
Answered by Vimala Ramamurthy | 15 Feb, 2015, 19:43: PM

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CBSE 12-science - Maths
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