Question

The Sorry State Lottery requires you to select five different numbers from 0 through 43. (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?

Answer 1

five numbers are to be chosen from 44 numbers (0 to 43) ,this can be done in 44C5 ways = 1086008

a)

Big Winner if the five numbers you select agree with those in the drawing

out of 5 winning numbers, 5 winning numbers are drawn , this can be done in 5C5 =1 way

P(big winner) = 1/1086008 = 0.000000921

b)

Small-Fry Winner if four of your five numbers agree with those in the drawing

out of 5 winning numbers, 4 winning numbers are drawn

out of (44-5)=39 non winning numbers,1 is chosen

this can be done in (39C1) way

so, P(small fry winner) = 5C4 * 39C1 / 44C5 = 195/1086008 = 0.000179557

c)

P(big winner + small fry winner) = 1/1086008 + 195/1086008 = 196/1086008=0.000180477