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CBSE Class 12-science Answered

A and B throw a pair of dice turn by turn. The first to throw 9 is awarded a prize. If A starts the  game, show rhat the probability of A getting the prize is 9/17
Asked by mishrapragu1998 | 14 Feb, 2016, 10:05: AM
answered-by-expert Expert Answer
begin mathsize 11px style Let space apostrophe straight A apostrophe space be space the space event space that space straight A space gets space the space prize. If space apostrophe straight A apostrophe space starts space the space game comma space he space can space get space proze space in space first space attempt space or space second space attempt space or space third space attempt space and space so space on comma provided space that space straight B space makes space unsuccessful space throws space in space between space straight A apostrophe straight s space attempts. So space the space probability space of space straight A space getting space prize equals straight P open parentheses straight A close parentheses plus straight P open parentheses top enclose straight A space top enclose straight B space straight A close parentheses plus straight P open parentheses top enclose straight A space top enclose straight B space top enclose straight A space top enclose straight B space straight A close parentheses plus..... So space first space we space have space to space find space the space probability space that space straight a space pair space of space dice space gives space an space outcome space of space 9 space in space any space throw. Total space number space of space cases equals 6 cross times 6 equals 36 Favorable space number space of space cases equals straight n open curly brackets open parentheses 3 comma 6 close parentheses comma space open parentheses 4 comma 5 close parentheses comma space open parentheses 5 comma 4 close parentheses comma space open parentheses 6 comma 3 close parentheses close curly brackets equals 4 So space the space probability space of space getting space award space in space any space throw equals 4 over 36 equals 1 over 9 So space the space probability space of space NOT space getting space award space in space any space throw equals 1 minus 1 over 9 equals 8 over 9 So space the space probability space of space apostrophe straight A apostrophe space gettting space the space prize equals straight P open parentheses straight A close parentheses plus straight P open parentheses top enclose straight A space top enclose straight B space straight A close parentheses plus straight P open parentheses top enclose straight A space top enclose straight B space top enclose straight A space top enclose straight B space straight A close parentheses plus..... equals 1 over 9 plus 8 over 9 cross times 8 over 9 cross times 1 over 9 plus 8 over 9 cross times 8 over 9 cross times 8 over 9 cross times 8 over 9 cross times 1 over 9 plus.... equals 1 over 9 plus open parentheses 8 over 9 close parentheses squared cross times 1 over 9 plus open parentheses 8 over 9 close parentheses to the power of 4 cross times 1 over 9 plus.... space left parenthesis an space infinite space straight G. straight P. space series space with space straight a equals 1 over 9 space and space straight r equals open parentheses 8 over 9 close parentheses squared right parenthesis equals fraction numerator begin display style 1 over 9 end style over denominator 1 minus open parentheses begin display style 8 over 9 end style close parentheses squared end fraction equals 1 over 9 cross times 81 over 17 equals 9 over 17 end style
Answered by satyajit samal | 15 Feb, 2016, 01:15: PM
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