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An unbiased die is tossed 3 times, suppo...

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)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let x be the random variable. sixes are consecutive

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