Question

The Sorry State Lottery requires you to select five different numbers from 0 through 55. (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

Number of different numbers from 0 to 55 =56

Number of different numbers available to select = 56

Number of different numbers to select = 5

Number of ways of selecting 5 numbers from 56 number =

Big Winner if the 5 numbers you select agree with those in the drawing, i.e Number of ways that the 5 numbers selected by you match with the 5 numbers drawn =

Probability of being a Big winner

= Probability that  the 5 numbers selected by you match with the 5 numbers drawn

= Number of ways that the 5 numbers selected by you match with the 5 numbers drawn / Number of ways of selecting 5 numbers from 56 number

= 1/3819816

Probability of being a Big winner =

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

i.e four of your five numbers match with four numbers in the drawing and the fifth number is not matching with the the five drawing numbers

=Number of ways of selecting 4 number from the 5 numbers that match; and selecting that one number from the remaining: 49 (54-5) numbers

=

Probability of being a Small-Fry Winner

= Probability that  the 4 of the 5 numbers selected by you match with those in the drawing

= Number of ways of selecting 4 number from the 5 numbers that match; and selecting that one number from the remaining:/ Number of ways of selecting 5 numbers from 56 number

= 245/3819816

Probability of being a Small-Fry Winner =

probability that you are either a Big Winner or a Small-Fry Winner

= probability that you are either a Big Winner + probability that you are either a a Small-Fry Winner

=

probability that you are either a Big Winner or a Small-Fry Winner