2016 AJC P2 Q6

An experiment is carried out with three coins. Two of the coins are fair. The third coin is biased such that the probability of obtaining a head is \(\frac{1}{5}\). The three coins are tossed.

\(A\) is the event: All the three coins show the same result.
\(B\) is the event: The biased coin shows a tail.

Find

1. \({P(A \cup B)}\),[3]
2. \({P(B'|A')}\).[3]