1 The Sorry State Lottery requires you to select five differ

1. The Sorry State Lottery requires you to select five different numbers from 0 through 63. (Order is not important.) You are a Big Winner if the five numbers you select agree with those in the drawing, and you are a Small-Fry Winner if four of your five numbers agree with those in the drawing. (Enter your answers as exact answers.)

What is the probability of being a Big Winner?


What is the probability of being a Small-Fry Winner?


What is the probability that you are either a Big Winner or a Small-Fry Winner?

Solution

There are 50 numbers in the draw (0-49).

Hence, there are 50C5 = 2118760 ways to guess.

Hence,

P(big) = 1/2118760 or 4.71974E-07 [ANSWER]

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For small fry, there are 5C4 = 5 ways to choose 4 correct among the 5, and then 45 other ways to choose a wrong one.

Hence, there are 45*5 = 225 ways.

hence,

P(small) = 225/2118760 = 0.000106194 [ANSWER]

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Hence,

P(big or small) = 0.000106194 + 4.71974E-07 = 0.000106666 [ANSWER]