4 A fair tetrahedral die has faces numbered \(1,2,3,4\). A coin is biased so that the probability of showing a head when thrown is \(\frac { 1 } { 3 }\). The die is thrown once and the number \(n\) that it lands on is noted. The biased coin is then thrown \(n\) times. So, for example, if the die lands on 3 , the coin is thrown 3 times.

1. Find the probability that the die lands on 4 and the number of times the coin shows heads is 2 .
2. Find the probability that the die lands on 3 and the number of times the coin shows heads is 3 .
3. Find the probability that the number the die lands on is the same as the number of times the coin shows heads.