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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. 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?

Respuesta :

The lottery requires you to select 5 different numbers from 0 through 59 which mean there are total 60 numbers. The possible way to draw 5 number out of 60 number would be: 60C5= 60!/5!55!= 5461512 ways

- What is the probability of being a Big Winner?
The big winner has 5 same number from 5 number, that was drawn. Then the probability would be: 5C5/ 60C5= 1/ 5461512

- What is the probability of being a Small-Fry Winner
Small fry winner needs to have 4 same number and 1 random number. The 4 number should be same from the 5 drawn number. The 1 random number should be drawn from the 55 number that wasn't drawn. The probability would be:
5C4 * 55C1/ 60C5=  5*55/5461512= 275/ 5461512

- What is the probability that you are either a Big Winner or a Small-Fry Winner?Since you can become big winner and small winner in same time, you just need to add the probability of both. The answer would be: 1+275/ 5461512= 276/ 5,461,512= 23/455,126

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