Official solution
Probability of fail, P(F) = p
\[ \therefore \] Probability of success, P(S) = 2p
We know,
p + 2Pp = 1
\[ \Rightarrow \] p = \[{1 \over 3}\]
\[ \therefore \] Now, probability of at least 5 success in 6 trials,
P(x \[ \ge \] 5)
= P(x = 5) + P (x = 6)
= 6C5 \[{\left( {{2 \over 3}} \right)^5}{\left( {{1 \over 3}} \right)^1}{ + ^6}{C_6}{\left( {{2 \over 3}} \right)^6}{\left( {{1 \over 3}} \right)^o}\]
= \[{\left( {{2 \over 3}} \right)^5}\left( {{6 \over 3} + {2 \over 3}} \right)\]
= \[{{256} \over {729}}\]