Daniel goes with his father to an amusement park and heads straight for the shooting game. He pays $3 to enter the game and he is offered five shots; if he finds the target in at least four of them, he wins a prize which his dad estimates to be worth $6.

Assuming that the probability of hitting the target in each shot is p, find Daniel’s

(or his dad’s!) expected profit if

(i) p = 0.7;

(ii) p = 0.9.