You must show all work lo earn credit So credit will be give

You must show all work lo earn credit. So credit will be given without supporting work A green, yellow. and red light are linked to a button. When the button is pushed either the green, yellow, or red light will light up and will do so independently of all other outcomes. A game is created using this system. You win the game by either pushing the button once and getting a green light, or pushing the button twice and getting either 2 green lights or exactly one red light. The probability of having the green light Hash on a single push is constant and three times the probability of the red light. Find the probability of having the green light flash it the probability ol winning is the same for cither the one-push or two-push option.

Solution

P( green light on a single push ) = 3 P( red light)

P( green ) = 1/3

P( green 2 times) = 1/3*1/3=1/9

1/3 + 1/9 = 4/9