Re: 2 ques.

Posted by Sinistral on May 29, 2013; 3:49pm
URL: http://discussion-forum.276.s1.nabble.com/2-ques-tp7580420p7581472.html

just read the explanation provided by duck

if success = S and Failure = F then he will succeed if one of the following happens:
S, FS, FFS, FFFS ....
Respective probabilities: 3/4 , (1/4)(3/4), (1/4)^2 (3/4), (1/4)^3(3/4)....
respective prizes:          2^1 , 2^2      ,    2^3           ,      2^4  ........

P(Success) = P(S)+ P(FS)+ P(FFS)+ P(FFFS) .... (write it using sigma.)
Expected value of gamblers's prize = P(S)*2^1 + P(FS)*2^2 + P(FFS)*2^3 + P(FFFS)*2^4 .....
            write the above in the sigma form and u will get the desired result (given in earlier post). Its basically a GP , so it can be easily summed till infinity to get the desired answer.