In a competition, people pay $1 to throw a ball at a target. If they hit the target on the first throw they receive $5. If they hit it on the second or third throw they receive $3, and if they hit it on the fourth or fifth throw they receive $1. People stop throwing after the first hit, or after 5 throws if no hit is made. Mario has a constant probability of \(\frac{1}{5}\) of hitting the target on any throw, independently of the results of other throws.

1. Mario misses with his first and second throws and hits the target with his third throw. State how much profit he has made.
2. Show that the probability that Mario’s profit is $0 is 0.184, correct to 3 significant figures.
3. Draw up a probability distribution table for Mario’s profit.
4. Calculate his expected profit.