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CBSE Class 11-science Answered

Two cards are drawn from a deck of 52 cards.what is the probability that a) both are of same colour .    B) at least one spade card..
Asked by Sahar | 23 Jan, 2016, 03:30: PM
answered-by-expert Expert Answer
begin mathsize 14px style W h e n space t w o space c a r d s space a r e space d r a w n space f r o m space a space p a c k space o f space 52 space c a r d s comma space n left parenthesis S right parenthesis equals C presuperscript 52 subscript 2 a right parenthesis space L e t space E space b e space t h e space e v e n t space t h a t space t w o space c a r d s space a r e space o f space t h e space s a m e space c o l o u r. N o w space t h e r e space a r e space 26 space b l a c k space c a r d s space a n d space 26 space r e d space c a r d s space i n space d e c k space o f space 52 space c a r d s. rightwards double arrow n left parenthesis E right parenthesis equals C presuperscript 26 subscript 2 plus C presuperscript 26 subscript 2 rightwards double arrow P left parenthesis E right parenthesis equals fraction numerator C presuperscript 26 subscript 2 plus C presuperscript 26 subscript 2 over denominator C presuperscript 52 subscript 2 end fraction equals 2 cross times fraction numerator C presuperscript 26 subscript 2 over denominator C presuperscript 52 subscript 2 end fraction equals 2 cross times fraction numerator begin display style fraction numerator 26 cross times 25 cross times 24 factorial over denominator 24 factorial cross times 2 cross times 1 end fraction end style over denominator begin display style fraction numerator 52 cross times 51 cross times 50 factorial over denominator 50 factorial cross times 2 cross times 1 end fraction end style end fraction equals fraction numerator 13 cross times 25 over denominator 26 cross times 51 end fraction equals 325 over 1326 equals 0.25 b right parenthesis space L e t space T space b e space t h e space e v e n t space t h a t space a t space l e a s t space o n e space o f space t h e m space i s space s p a d e. T h e n comma space T apostrophe space i s space t h e space e v e n t space t h a t space n o n e space o f space t h e m space i s space s p a d e. rightwards double arrow n left parenthesis T right parenthesis equals C presuperscript 39 subscript 2 rightwards double arrow P left parenthesis T apostrophe right parenthesis equals fraction numerator C presuperscript 39 subscript 2 over denominator C presuperscript 52 subscript 2 end fraction equals fraction numerator begin display style fraction numerator 39 cross times 38 cross times 37 factorial over denominator 37 factorial cross times 2 cross times 1 end fraction end style over denominator begin display style fraction numerator 52 cross times 51 cross times 50 factorial over denominator 50 factorial cross times 2 cross times 1 end fraction end style end fraction equals fraction numerator 39 cross times 19 over denominator 26 cross times 51 end fraction equals 741 over 1326 equals 0.56 rightwards double arrow P left parenthesis T right parenthesis equals 1 minus P left parenthesis T apostrophe right parenthesis equals 1 minus 0.56 equals 0.44 end style
Answered by Rashmi Khot | 25 Jan, 2016, 10:53: AM

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