Question 1. Mini Powerball There are five balls in an urn. They are enumerated 1

Question

Question 1. Mini Powerball

There are five balls in an urn. They are enumerated 1,2,3,4,5. We pull three balls out of the urn without replacing it. Those three balls are winning combination. (The winning combination is 1,2,3 order does not matter)

For all three numbers you win a Powerball’s jackpot. For two numbers you win $100, and for 1 number $2.

A) What are the chances you guess all 3 numbers? Recall the order does not matter.

B) What are the chances to guess exactly two out of three numbers?

C) What are the chances to guess exactly one out of three numbers?

D)

Here are all the odds of winning in the Powerball. On internet the chances of winning are given in this table below. Your task is to check that these odds are right and to show in detail how they are computed

Match Prize Odds Grand Prize $1,000,000 $50,000 $100 $100 $7 $7 $4 $4 1 in 292.201.338.00 1 in 11.688.053.52 in 913,129.18 1 in 36,525.17 1 in 14.494.11 1 in 579.76 1 in 701.33 1 in 91.98 1 in 38.32 The overall odds of winning a prize are 1 in 24.87 The odds presented here are based on a $2 play (rounded to two decimal places)

Explanation / Answer

If all 3 numbers are the same

prob = 1/5C3 = 1/10

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B) Prob for guessing exactly any 2 numbers = 3C2/5C2 = 3/10

C) Prob for guessing exactly any 2 numbers = 3C1/5C2 = 3/10

D) Odds for winning grand prize = 3/7 =

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