Official solution
An unbiased coin is tossed 8 times which is same as 8 coins tossed 1 times.
\[\therefore\,\,\,\] Possible no. of out come = 28
\[\therefore\,\,\,\] Sample space = 28
Here in this condition, all head or all tail out come is not acceptable.
No. of times all head can occur
(H H H H H H H H) = 1
\[\therefore\,\,\,\] Probability (all head) = \[{1 \over {{2^8}}}\] = \[{1 \over {256}}\]
No. of times all tail can occur
(T T T T T T T T) = 1
\[\therefore\,\,\,\] Probability (all tail) = \[{1 \over {{2^8}}}\] = \[{{1 \over {256}}}\]
\[\therefore\,\,\,\] Required probability
= 1 - (P (All head) + P (All tail))
= 1 - ( \[{{1 \over {256}}}\] + \[{{1 \over {256}}}\])
= 1 - \[{{1 \over {128}}}\]
= \[{{127} \over {128}}\]