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 57. (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 totally 58 numbers

1. No of ways of selecting 5 nos from 58 nos is = 58 C5---(1)

hence the prbability of being a big winner = 5 C5  / 58C5 = 1/ 58C5   ( probability is very small)

2. The probability of being small winnr = 5C4 / 58 C5 = 5/ 58 c5   

3 the above 2 events are mutually exclusive .

hence probability of being big or small winner = 1/ 58C5   + 5/ 58C5 = 6 / 58C5

  

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