The Sorry State Lottery requires you to select five different numbers from 0 thr

Question

The Sorry State Lottery requires you to select five different numbers from 0 through 50. (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?

Explanation / Answer

There are 51 numbers so nuber of ways of selecting 5 numbers out of 50 is

C(51,5) = 2349060

Out of these possible, only one combination is corresponidng to big winner so the probabiliyt of being a big winner is

P(big winner) = 1 / 2349060

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Number of ways of slecting 4 numbers out of 5 selected numbers is C(5,4) = 5. So

P(Small fry winner) = 5 / 2349060

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You can be either big winner or small Fry winner not both so

P(big winner or small Fry winner) = P(big winner) + P(Small fry winner) = 6 / 2349060

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