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

Question

3. The Sorry State Lottery requires you to select five different numbers from 0 through 59. (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

a) In all there are 60C5 possibilities.

Probability of being a Big winner = 1 / 60C5 = 1 / 5461512

= 0.0000001831

b) One can be a Small fry winner in 5C4 * 55C1 / 60C5 = 5 * 55 / 5461512

Probability of being a Small fry winner

= 0.00005035

c) Probability of being either a Big Winner or a Small-Fry Winner

= 1 / 5461512 + 275 / 5461512

= 276 / 5461512

= 0.00005053.

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