Powerball is a game of chance that has generated intense interest because of its large jackpots. To play this game, a player selects five different numbers from 1 through 59, and then picks a Powerball number from 1 through 39. The lottery organization randomly draws 5 different white balls from 59 balls numbered 1 through 59, and then randomly picks a Powerball number from 1 through 39. It is possible for the Powerball number to be the same as one of the first five numbers.
a. If a player’s first five numbers match the numbers on the five white balls drawn by the lottery organization and the player’s Powerball number matches the Powerball number drawn by the lottery organization, the player wins the jackpot. Find the probability that a player who buys one ticket will win the jackpot.
b. If a player’s first five numbers match the numbers on the five white balls drawn by the lottery organization, the player wins about $200,000. Find the probability that a player who buys one ticket will win this prize.