The Sad State Lottery requires you to select a sequence of three different numbe

Question

The Sad State Lottery requires you to select a sequence of three different numbers from 0 through 59. (Order is important.) You are a Winner if your sequence agrees with that in the drawing, and you are a Booby Prize Winner if your selection of numbers is correct, but in the wrong order. (Enter your answers as exact answers.) What is the probability of being a Winner?


What is the probability of being a Booby Prize Winner?


What is the probability that you are either a Winner or a Booby Prize Winner?

Explanation / Answer

Probability of becoming Winner (A)= 1 / (60P3)

[60P3 because the order is important]

= 1 / [60! / (57!)] = 0.00000487

Probability of being a Booby Prize Winner (B)= 1 / 60C3

[60C3 because the order is not important]

= 1 / [60! / (57!)(3!)] = 0.00002922

Probability that you are either a Winner or a Booby Prize Winner = P(A U B) = P(A) + P(B) - P(A and B)

P(A and B) = P(A) as being a winner and booby prize winner is the same as being the winner.

So, Probability that you are either a Winner or a Booby Prize Winner = P(A) + P(B) - P(A)

= P(B) = 0.00002922

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