This is my first post here. I need help with my math homework. I had to create the problem, but I don't know how to answer it.

At the carnival, there is a board with a spinner. It costs $3 to play this game and you receive $6 if you win. There are 4 green tiles on the board and 6 blue. Each player has 2 spins. In order to win, the player must spin one of each color. They must spin a green, then blue, or spin a blue, then green. If they get two of the same color, they lose.

- Figure out the expected value for the game (cost of game minus cost of price) to show the profit the carnival should expect to make over the long haul if the game is enticing enough for people to play.

... I am assuming I need to find the probability of spinning a green , then blue, or blue, then green.. but I do not know how to do this. Thank you for taking the time to read this and any help showing how to do it is greatly appreciated.