1. The problem statement, all variables and given/known data An electric circuit has 5 components. It is known that one of the componenets is faulty. To detremine which one is faulty, all 5 componenets are tested one by one until the faulty component is found, The random variable X represents the number of test required to determine the faulty unit. 2. Relevant equations 3. The attempt at a solution here's my working: I let X = number of tests conducted until the faulty unit is found P(X= 1) = 1/5 P(X=2) = P(good) x P( faulty ) = 4/5 x 1/5 = 0.16 P(X=3) = P(good) x P(good) x P( faulty ) = 4/5 x 4/5 x 1/5 = 0.128 P(X=4) = P(good) x P(good) x P(good) x P( faulty ) = 4/5 x 4/5 x 4/5 x 1/5 = 64/625 P(X=5) = P(good) x P(good) x P(good) x P(good) x P( faulty ) = 4/5 x 4/5 x 4/5 x 4/5 x 1/5 = 256/3125 But for the discrete probablity distributions , sum of all probability must be equal to 1 ... my sum of probability isn't equal to 1 , which is indeed wrong. why cant i do in this way?