Show your calculations and logic - and USE EXCEL FORMULAS to solve the following problems where applicable.

You have received an invitation to take part in a game show hosted by your local TV station. The game show consists of three rounds the participant goes through.

Round 1: The participant is shown a large television screen having 3 equal sized blanked out squares. The squares hide behind them either a "Green" light or a "Red" light. There is equal probability of a square having either a "Green" light or a "Red" light.

The crowd watching the game show is all excited and the host presses a button to reveal all the three lights hiding behind the squares. If there is a green light in any of the squares the participant wins $1000 and also gets to advance to the next round, else the participant gets eliminated without getting any money.

Round 2: The participant is to select one door from the three closed doors shown. The doors hide behind them three different paths. One of the door leads to a Basketball court, the remaining doors lead to exits from the game show. If the door selected by the participant leads to the Basketball court, the participant is offered a choice of $5000 or "advancing to the next round" (but not both). If the door selected by the participant does not lead to a Basketball court, the person gets eliminated.

Round 3: In this round the participant shoots baskets from the 3-point line in a basketball court for 3 minutes (a continuous supply of basketballs being readily available). For every basket scored the participant gets an amount of $1000.

You are in need to raise a minimum $6000 for a home improvement project of yours. You are also a good basketball player and wonder if this is a good opportunity to get the money you need. You check on your shooting ability by going to the gym and figure out that if a continuous supply of basketballs is readily available, on average you can score 10 baskets from the 3-point line in 5 minutes.

You decide to take part in the game show.

[HINT:Use a Binomial Distribution for round 1 probabilities and a Poisson Distribution for Round 3 probabilities]

(a) Given that you have reached Round 3, what are the chances of you meeting your money needs for the home improvement project. Briefly show your calculations.

(b)Let's say you decide before the game show starts that if you win Round 2 then you will quit (since you would have made your $6000).

What is the probability of you meeting your money needs for the home improvement project. Briefly show your calculations.

(c)Your friend Sam also wants to participate in the game show. His shooting prowess is same as yours. What would you advise him is the probability of his making at least $7000 from the game show? Briefly show your calculations.

(d)What would be Sam's probability of making no money in the game show? Briefly show your calculations.