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CBSE Class 12-science Answered

Two numbers b and c are chosen at random with replacement from the numbers 1 to 9.  Find the probability that x^2 + bx + c > 0 for all x beloging to R
Asked by Shruthi Vidya | 06 Jul, 2014, 08:03: PM
answered-by-expert Expert Answer

I n space o r d e r space t o space h a v e space q u a d r a c t i c space i n e q u a l t i y space p o s i t i v e space f o r space a l l space v a l u e s space o f space x Q E space s h o u l d space b e space i n space f o r m space o f space open parentheses x plus-or-minus k close parentheses squared plus C space w h e r e space C greater than 0 N o w space i n space g i v e n space q u e s t i o n space x squared plus b x plus c greater than 0 I f space w e space t a k e space b equals 9 space t h e n space x squared plus 2 open parentheses 9 over 2 close parentheses x plus open parentheses 9 over 2 close parentheses squared space b u t space c space c a n n o t space t a k e space m o r e space t h a n space 9. space S o space t h i s space c a s e space i s space n o t space p o s s i b l e S i m i l a r l y space f o r space 6 comma space 7 comma space 8 space a n d space 9 space n o space v a l u e space i s space p o s s i b l e space f o r space c W h e n space w e space t a k e space b equals 5 comma space C space c a n space t a k e space 7 comma space 8 space a n d space 9 space b e c a u s e space space x squared plus 2 open parentheses 5 over 2 close parentheses x plus open parentheses 5 over 2 close parentheses squared space w h e r e space 7 comma space 8 space a n d space 9 space c a n space b e space s p l i t space i n t o space s u m space o f space t w o space n u m b e r s space w i t h space v a l u e s space 6.25 plus k S i m i l a r l y space f o r space b equals 4 comma space C space c a n space t a k e space 5 comma space 6 comma space 7 comma space 8 comma space 9 b equals 3 comma space C space c a n space t a k e space 3 comma space 4 comma space 5 comma space 6 comma space 7 comma space 8 comma space 9 b equals 2 comma space C space c a n space t a k e space 2 comma space 3 comma space 4 comma space 5 comma space 6 comma space 7 comma space 8 comma space 9 b equals 1 comma space C space c a n space t a k e space a l l space 1 minus 9 S o space n u m b e r space o f space p o s s i b i l i t e s space i n space f a v o u r space a r e space 3 plus 5 plus 7 plus 8 plus 9 equals 32 T o t a l space c h a n c e s space p o s s i b l e equals 9 cross times 9 equals 81 P r o b a b i l i t y equals 32 over 81 space

Answered by Dharma Teja | 07 Jul, 2014, 10:40: AM

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CBSE 12-science - Maths
The probability that a pen manufactured by a company will be defective is 0.1. If 12 such pens are selected find the probability that i) exactly 2 will be detective ii) at least 2.will be defective iii)none will he defective
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the question and the solution is in the attachment, can you explain how can they use combinations when combinations does not account for replacement while it is mentioned in the question that replacement is to be taken into account? And can you provide the correct answer.
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CBSE 12-science - Maths
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CBSE 12-science - Maths
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