Powerball is a jackpot game with a grand prize starting at $20 million and often rolling over into the hundreds of millions. In 2006, the jackpot was $365 million.
The winner may choose to receive the jackpot prize paid over 29 years or as a lump-sum payment. For $1 the player selects six numbers for the base game of Powerball. There are two independent stages of the game. Five balls are randomly drawn from 59 consecutively numbered white balls. Moreover, one ball, called the Powerball, is randomly drawn from 39 consecutively numbered red balls. To be a winner, the numbers selected by the player must match the numbers on the randomly drawn white balls as well as the Powerball.
a. What is the probability that the player is able to match the numbers of two out of five randomly drawn white balls?
b. What is the probability that the player is able to match the numbers of all five randomly drawn white balls?
c. What is the probability that the player is able to match the Powerball for a randomly drawn red ball?
d. What is the probability of winning the jackpot?