The Sorry State Lottery requires you to select five differen

The Sorry State Lottery requires you to select five different numbers from 0 through 60. (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.

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

What is the probability of being a Big Winner?

There are 61 numbers here. Thus, there are 61C5 ways to choose any 5 numbers.

Thus,

P(big winner) = 1/(61C5) = 0.000000168091 [ANSWER]

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

There are 5C4 = 5 ways to choose 4 correct numbers, and 56 ways to choose 1 incorrect number. Thus,

P(small-fry winner) = [(5)(56)]/(61C5) = 0.0000470656 [ANSWER]

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

Thus,

P(big winner or small fry winner) = 0.000000168091 + 0.0000470656 =    0.0000472337 [ANSWER]