Question

An experiment succeeds twice as often as it fails.The chance thatg in next six trails there shall be at least 4 success is ?

Answer 1

let probablity of sucess = p

and that of failure = q

given  A/Q ⇒  p =2q        and    aslo  p+q = 1 

                   that gives  p = 2/3      and    q = 1/3 
              

now question asking at least 4 success ⇒  P(n=4) + P( n =5) + P(n=6)

           P(n=x)  =  ⁿCₓ (p)ˣ (q)ⁿ⁻ˣ            here n= 6

so ans  =  ⁶C₄ (2/3)⁴ (1/3)² + ⁶C₅(2/3)⁵(1/3)¹ + ⁶C₆(2/3)⁶(1/3)⁰

                 = 15. 16/81. 1/9 + 6 . 32/243 . 1/3 + 1. 64/729 .1 =  493/729



hope that correct ans = c) 496/729