An unbiased die is tossed 3 times, suppose that a variable x is assigned the value k, when k consecutive sixes are obtained for else x takes the value –1 . Then expected value of x is:

A. `(182)/(216)`
B. `(172)/(216)`
C. `(-182)/(216)`
D. `-(172)/(216)`

Options

A. `(182)/(216)`
B. `(172)/(216)`
C. `(-182)/(216)`
D. `-(172)/(216)`

Answer

C

Explanation

Let x be the random variable . X = k sixes are consecutive .

Let S = Getting six on die and F Getting no six .
Sample point FFF `rArr x = 0 = (5^(3))/(6^(3))`
SFS + 3(SFF) `rArr = x =1 = 3(5^(2))/(6^(2)) (1)/(6) + (5)/(216) = (80)/(2016)`
SSF,FSS `rArr x = 2 =(10)/(2016)`
` SSS " " rArr " "x = 3 = (1)/(216)`
Mean `= sum x P(x) = (182)/(216)`