A carnival game in London offers £100 cash prize to anyone who bursts a balloon by throwing a dart at it. It costs £5 to throw a dart. The game is over once a player bursts a balloon or their money runs out. Ex-World No. 1 professional darts player Phil Taylor has won 14 world championships and over £7 million in prize money. Assume that Phil Taylor has a 90% chance of bursting a balloon on any throw. His wife only allows him to spend £20 at this game.
1. What is the probability that Phil Taylor bursts a balloon on the 4th throw?
2. What is the probability that Phil Taylor bursts a balloon on the 2nd or 3rd throw?
3. What is the probability that Phil Taylor loses all the money that his wife gave him at this game?
4. Use the information from parts 1 to 3 to tabulate the probability distribution for the amount of money Phil Taylor wins at this game. Hints: If Phil bursts a balloon on the 2nd attempt, then the amount of money he wins is 100 - 5 -5 = 90. Click INSERT above next to FILE, HOME and click Table if you want to draw a table.
5. Using information from part 4, How much money do you expect Phil Taylor to win at this game?
6. Using information from part 4, what is the standard deviation for the amount of money Phil Taylor wins at this game?