A biased die is marked with numbers 2 , 4 , 8 , 16 , 32 , 32 on its faces and the probability of getting a face with mark n is 1 n . If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48 , is

Step-by-step solution

P 2 = 1 2 , P 4 = 1 4 , P 8 = 1 8 , P 16 = 1 16 , P 32 = 1 32 When we get the faces as 8 , 8 , 32 then the probability will be 3 1 8 × 1 8 × 2 32 = 3 1024 When we get the faces as 16 , 16 , 16 then the probability will be 1 16 × 1 16 × 1 16 = 1 4096 Hence, the required probability will be 3 1024 + 1 4096 = 13 4096