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Calculating Probabilities in a Powerball Lottery Game

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Powerball is a lottery game. It involves choosing five white balls from a drum containing 55 balls and one red ball from a drum containing 42 balls. A player must match all five white balls and the red ball to win the jackpot.

How would you investigate the question about the probability of matching only the red ball?

What statistical methods in this chapter would you use?
Combination method
nCr = n! / (n-r!) *r!

Show the calculations you would use to answer the question.

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Let A be the event "none of the white balls match" and B be the event "the red ball matches". ...

Solution Summary

The solution shows how to calculate probabilities using combinations.

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The solution gives detailed steps on calculating probabilities in the case of power-ball under different conditions.

The game of PowerBall goes like this: 5 white balls are drawn from one drum that contains 42 balls. One red ball (the powerball) is drawn from a separate drum that contains 20 balls. To win the jackpot, you must have all 5 white balls correct as well as the red powerball. No balls are replaced after being drawn. The order you have your numbers in does not matter. For example, if the numbers drawn from the white drum were 9, 8, 1, 3, and 6 and your numbers were 1 3 6 8 9 , you would still be a winner. Express all final answers in either lowest fraction form, or a decimal in standard form.

a. Find the probability of being a jackpot winner. You must show all work to show how you and your partner got the answer. There is more than one way to do this problem.

b. Would it make a huge difference in the probability if the order of the numbers did matter? (meaning you had to pick the 5 numbers in the same order as they were drawn from the drum) Find this probability of winning the jackpot if the order did matter and compare it to part a. You must show all work to show how you got your answer.

c. You can win $500,000 if you get all the white balls correct(in any order), but get the red ball wrong. What are the chances of winning $500,000? You must show all work to show how you got your answer.

d. Do you have a better chance of winning the $500,000 as explained above, or playing a lottery that doesn't even have the red powerball at all. Assume everything else about this other lottery is the same as explained in the beginning of this problem. You must show all work to show how you got your answer.

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