Question

Beginning in October, 2015, Powerball® became an even larger combined large jackpot game and cash game. Every Wednesday and Saturday night at 10:59 p.m. Eastern Time, five white balls are drawn out of a drum with 69 balls and one red ball out of a drum with 26 red balls.

There are two bins—one containing white balls, and one containing red balls. When a player fills out a ticket, he or she selects five numbers from the set of white balls (1–69) and one number from the set of red balls (1-26). Prizes awarded to players are based on how many balls of each color are matched. If all five white ball numbers and the colored ball number are matched, the player wins the jackpot. If more than one player matches all of the numbers, then the jackpot is divided among them.

1) What is the probability of winning the jackpot?

2) Suppose if the player wins the jackpot, her prize will be $140,000,000. If a she doesn’t win the jackpot, she will get nothing and thus effectively lose $2 for purchasing the ticket. What is her expected earnings/loss if she buys one ticket?

Answer 1

ANSWER::

1).

Probability of winning the jackpot is given by

2).

Suppose, random variable X denotes amount gained (in dollar).

Her expected loss is   $ 1.520878.

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