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 needs to choose between two doors (one of which has a $1000 behind it). If the participant choses the correct door he/she gets to keep the $1000 and also advance to the next round, else the participant gets eliminated.

Round 2: The game show host will roll a fair dice 10 times and after the host has rolled it the 10^thtime the participant is shown the results of all the 10 rolls. If participant gets a "6" on at least three of the rolls he/she is offered a choice of $5000 or "advancing to the next round" (but not both). If the participant does not get a "6" on at least three of the rolls the person gets eliminated.

Round 3: In this round the participant shoots baskets from the free throw line in a basketball court for 2 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 $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 16 baskets from the free throw line in 5 minutes.

You decide to take part in the game show.

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 and state any assumptions that you make.