Question

Let’s suppose that you are going to play the lottery game Powerball. To play, you pick five different numbers from 1 through 69 plus one Powerball number from 1 through 26. Which is a more likely combination of winning numbers: 1, 2, 3, 4, 5, 6 or 7, 21, 25, 32, 40, 56? Explain your answer. For a $500,000,000 jackpot, which of the two combinations would likely be more lucrative for you if it were to win? In other words, for which combination would you be less likely to have to split the jackpot with other players who also had the winning combination? Of the two combinations above, which would you be more likely to play? Why?

Answer 1

There are a total of 95 balls.
Of these 95 balls, there are 2 balls each numbered 1 through 26, and 1 ball each numbered 27 to 69.
Let X be a random variable denoting the number observed on the ball.
Hence,

• Scenario 1: Balls chosen are 1,2,3,4,5,6.
  Hence, probability of winning:
  
  
  
• Scenario 2: Balls chosen are 7,21,25,32,40,56.
  Hence, probability of winning:
  
  
  

Hence, we observe that, . Hence, choosing balls 1,2,3,4,5 and 6 is more lucrative than choosing balls 7,21,25,32.40 and 56 since it has higher probability.

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