27. Five mark exercise problem X

In a game, the entry fee is \(₹\)150. The game consists of tossing a coin \(3\) times. Dhana bought a ticket for entry. If one or two heads shows she gets her entry fee back. If she throws \(3\) heads, she receives double the entry fees. Otherwise, she will lose.

 

Find the probability that she:

 

i) Gets double entry fee \(=\) $\frac{i}{i}$

ii) Just gets her entry fee \(=\) $\frac{i}{i}$

iii) Loses the entry fee \(=\) $\frac{i}{i}$