In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to :

Step-by-step solution

The probability of getting a 4 in a throw of a die is 1 6 . The probability of getting other than 4 i.e. 4 i.e. numbers 1 ,   2 ,   3 ,   5 &   6 in a single throw of a die is 5 6 . Total throws done = 5 . For the event to be completed in 5 t h throw, 4 t h and 5 t h throw must be 4 . Also, 3 r d throw must be other than 4 i.e. 4 . Hence, cases for the first two position can be : Case I : 1 s t throw must be 4 and 2 n d throw must not be 4 i.e. 4 Thus, P 4 4 - 4 - 44 = 1 6 . 5 6 . 5 6 . 1 6